Page 1 Q u e s t i o n : 2 3 Mark the correct alternative in each of the following: The probability of an impossible event is a 1 b 0 c less than 0 d greater than 1 S o l u t i o n : We have to find the probability of an impossible event. Note that the number of occurrence of an impossible event is 0. This is the reason that’s why it is called impossible event. Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that n is a positive integer, it can’t be zero. So, whatever may be the value of n, the probability of an impossible event is . Hence the correct option is b. Q u e s t i o n : 2 4 The probability of a certain event is a 0 Page 2 Q u e s t i o n : 2 3 Mark the correct alternative in each of the following: The probability of an impossible event is a 1 b 0 c less than 0 d greater than 1 S o l u t i o n : We have to find the probability of an impossible event. Note that the number of occurrence of an impossible event is 0. This is the reason that’s why it is called impossible event. Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that n is a positive integer, it can’t be zero. So, whatever may be the value of n, the probability of an impossible event is . Hence the correct option is b. Q u e s t i o n : 2 4 The probability of a certain event is a 0 b 1 c greater than 1 d less than 0 S o l u t i o n : We have to find the probability of a certain event. Note that the number of occurrence of an impossible event is same as the total number of trials. When we repeat the experiment, every times it occurs. This is the reason that’s why it is called certain event. Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that n is a positive integer, it can’t be zero. So, the probability of an impossible event is . Hence the correct option is b. Q u e s t i o n : 2 5 The probability an event of a trial is a 1 b 0 c less than 1 d more than 1 S o l u t i o n : Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that m is always less than or equal to n and n is a positive integers, it can’t be zero. But, m is a non negative integer. So, the maximum value of probability of an event is , which is the probability of a certain event and the minimum value of it is 0, which is the probability of an impossible event. For any other events the value is in between 0 and 1. Hence the correct option is c. Q u e s t i o n : 2 6 Which of the following cannot be the probability of an event? a Page 3 Q u e s t i o n : 2 3 Mark the correct alternative in each of the following: The probability of an impossible event is a 1 b 0 c less than 0 d greater than 1 S o l u t i o n : We have to find the probability of an impossible event. Note that the number of occurrence of an impossible event is 0. This is the reason that’s why it is called impossible event. Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that n is a positive integer, it can’t be zero. So, whatever may be the value of n, the probability of an impossible event is . Hence the correct option is b. Q u e s t i o n : 2 4 The probability of a certain event is a 0 b 1 c greater than 1 d less than 0 S o l u t i o n : We have to find the probability of a certain event. Note that the number of occurrence of an impossible event is same as the total number of trials. When we repeat the experiment, every times it occurs. This is the reason that’s why it is called certain event. Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that n is a positive integer, it can’t be zero. So, the probability of an impossible event is . Hence the correct option is b. Q u e s t i o n : 2 5 The probability an event of a trial is a 1 b 0 c less than 1 d more than 1 S o l u t i o n : Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that m is always less than or equal to n and n is a positive integers, it can’t be zero. But, m is a non negative integer. So, the maximum value of probability of an event is , which is the probability of a certain event and the minimum value of it is 0, which is the probability of an impossible event. For any other events the value is in between 0 and 1. Hence the correct option is c. Q u e s t i o n : 2 6 Which of the following cannot be the probability of an event? a 1 3 b 3 5 c 5 3 d 1 S o l u t i o n : Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that m is always less than or equal to n and n is a positive integers, it can’t be zero. But, m is a non negative integer. So, the maximum value of probability of an event is , which is the probability of a certain event and the minimum value of it is 0, which is the probability of an impossible event. For any other events the value is in between 0 and 1. All the options except c satisfy the above criteria’s. Hence the correct option is c. Q u e s t i o n : 2 7 Two coins are tossed simultaneously. The probability of getting atmost one head is a 1 4 b 3 4 c 1 2 d 1 4 S o l u t i o n : The random experiment is tossing two coins simultaneously. Page 4 Q u e s t i o n : 2 3 Mark the correct alternative in each of the following: The probability of an impossible event is a 1 b 0 c less than 0 d greater than 1 S o l u t i o n : We have to find the probability of an impossible event. Note that the number of occurrence of an impossible event is 0. This is the reason that’s why it is called impossible event. Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that n is a positive integer, it can’t be zero. So, whatever may be the value of n, the probability of an impossible event is . Hence the correct option is b. Q u e s t i o n : 2 4 The probability of a certain event is a 0 b 1 c greater than 1 d less than 0 S o l u t i o n : We have to find the probability of a certain event. Note that the number of occurrence of an impossible event is same as the total number of trials. When we repeat the experiment, every times it occurs. This is the reason that’s why it is called certain event. Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that n is a positive integer, it can’t be zero. So, the probability of an impossible event is . Hence the correct option is b. Q u e s t i o n : 2 5 The probability an event of a trial is a 1 b 0 c less than 1 d more than 1 S o l u t i o n : Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that m is always less than or equal to n and n is a positive integers, it can’t be zero. But, m is a non negative integer. So, the maximum value of probability of an event is , which is the probability of a certain event and the minimum value of it is 0, which is the probability of an impossible event. For any other events the value is in between 0 and 1. Hence the correct option is c. Q u e s t i o n : 2 6 Which of the following cannot be the probability of an event? a 1 3 b 3 5 c 5 3 d 1 S o l u t i o n : Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that m is always less than or equal to n and n is a positive integers, it can’t be zero. But, m is a non negative integer. So, the maximum value of probability of an event is , which is the probability of a certain event and the minimum value of it is 0, which is the probability of an impossible event. For any other events the value is in between 0 and 1. All the options except c satisfy the above criteria’s. Hence the correct option is c. Q u e s t i o n : 2 7 Two coins are tossed simultaneously. The probability of getting atmost one head is a 1 4 b 3 4 c 1 2 d 1 4 S o l u t i o n : The random experiment is tossing two coins simultaneously. All the possible outcomes are HH, HT, TH, and TT. Let A be the event of getting at most one head. The number of times A happens is 3. Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Therefore, we have So, the correct choice is b. Q u e s t i o n : 2 8 A coin is tossed 1000 times, if the probability of getting a tail is 3/8, how many times head is obtained? a 525 b 375 c 625 d 725 S o l u t i o n : The total number of trials is 1000. Let x be the number of times a tail occurs. Let A be the event of getting a tail. The number of times A happens is x. Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Therefore, we have . But, it is given that . So, we have Page 5 Q u e s t i o n : 2 3 Mark the correct alternative in each of the following: The probability of an impossible event is a 1 b 0 c less than 0 d greater than 1 S o l u t i o n : We have to find the probability of an impossible event. Note that the number of occurrence of an impossible event is 0. This is the reason that’s why it is called impossible event. Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that n is a positive integer, it can’t be zero. So, whatever may be the value of n, the probability of an impossible event is . Hence the correct option is b. Q u e s t i o n : 2 4 The probability of a certain event is a 0 b 1 c greater than 1 d less than 0 S o l u t i o n : We have to find the probability of a certain event. Note that the number of occurrence of an impossible event is same as the total number of trials. When we repeat the experiment, every times it occurs. This is the reason that’s why it is called certain event. Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that n is a positive integer, it can’t be zero. So, the probability of an impossible event is . Hence the correct option is b. Q u e s t i o n : 2 5 The probability an event of a trial is a 1 b 0 c less than 1 d more than 1 S o l u t i o n : Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that m is always less than or equal to n and n is a positive integers, it can’t be zero. But, m is a non negative integer. So, the maximum value of probability of an event is , which is the probability of a certain event and the minimum value of it is 0, which is the probability of an impossible event. For any other events the value is in between 0 and 1. Hence the correct option is c. Q u e s t i o n : 2 6 Which of the following cannot be the probability of an event? a 1 3 b 3 5 c 5 3 d 1 S o l u t i o n : Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Note that m is always less than or equal to n and n is a positive integers, it can’t be zero. But, m is a non negative integer. So, the maximum value of probability of an event is , which is the probability of a certain event and the minimum value of it is 0, which is the probability of an impossible event. For any other events the value is in between 0 and 1. All the options except c satisfy the above criteria’s. Hence the correct option is c. Q u e s t i o n : 2 7 Two coins are tossed simultaneously. The probability of getting atmost one head is a 1 4 b 3 4 c 1 2 d 1 4 S o l u t i o n : The random experiment is tossing two coins simultaneously. All the possible outcomes are HH, HT, TH, and TT. Let A be the event of getting at most one head. The number of times A happens is 3. Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Therefore, we have So, the correct choice is b. Q u e s t i o n : 2 8 A coin is tossed 1000 times, if the probability of getting a tail is 3/8, how many times head is obtained? a 525 b 375 c 625 d 725 S o l u t i o n : The total number of trials is 1000. Let x be the number of times a tail occurs. Let A be the event of getting a tail. The number of times A happens is x. Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Therefore, we have . But, it is given that . So, we have Hence a tail is obtained 375 times. Consequently, a head is obtained times. So, the correct choice is c. Q u e s t i o n : 2 9 A dice is rolled 600 times and the occurrence of the outcomes 1, 2, 3, 4, 5 and 6 are given below: Outcome 1 2 3 4 5 6 Frequency 200 30 120 100 50 100 The probability of getting a prime number is a 1 3 b 2 3 c 49 60 d 39 125 S o l u t i o n : The total number of trials is 600. Let A be the event of getting a prime number 2, 3and5 . The number of times A happens is . Remember the empirical or experimental or observed frequency approach to probability. If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted by and is given by Therefore, we have So, the correct choice is a.Read More

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