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**NCERT TEXTBOOK QUESTIONS SOLVED**

**EXERCISE 15.1**

**Q 1. Complete the following statements: ****(i) Probability of an event E + Probability of the event â€˜not Eâ€™ = ________(ii) The probability of an event that cannot happen is ________. Such an event is called ________(iii) The probability of an event that is certain to happen is ________ Such an event is called ________(iv) The sum of the probabilities of all the elementary events of an experiment is ________(v) The probability of an event is greater than or equal to ________ and less than or equal to ________**

(ii) The probability of an event that cannot happen is 0. Such an event is called impossible event.

(iii) The probability of an event that is certain to happen is 1. Such an event is called sure or certain event.

(iv) The sum of the probabilities of all the elementary events of an experiment is 1.

(v) The probability of an event is greater than or equal to 0 and less than or equal to 1.

**Q 2. Which of the following experiments have equally likely outcomes? Explain. ****(i) A driver attempts to start a car. The car starts or does not start.(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.(iii) A trial is made to answer a true-false question. The answer is right or wrong.(iv) A baby is born. It is a boy or a girl.**

(ii) The player may shoot or miss the shot.

âˆ´ The outcomes are not equally likely.

(iii) In advance it is known that the answer is to be either right or wrong.

âˆ´ The outcomes right or wrong are equally likely to occur.

(iv) In advance it is known the newly born baby has to be either a boy or a girl.

âˆ´ The outcomes either a boy or a girl are equally likely to occur.

**Q 3. Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?****Sol. **Since on tossing a coin, the outcomes â€˜headâ€™ and â€˜tailâ€™ are equally likely, the result of tossing a coin is completely unpredictable and so it is a fair way.

**Q 4. Which of the following cannot be the probability of an event?****(A) 2/3 ****(B) âˆ’ 1.5 ****(C) 15% ****(D) 0.7****Sol.** Since, the probability of an event cannot be negative,

âˆ´ option **(B)**** âˆ’1.5** cannot be the probability of an event.

**Q 5. If P(E) = 0.05, what is the probability of â€˜not Eâ€™?****Sol.** âˆµ P(E) + P(not E)=1

âˆ´ 0.05 + P(not E)=1 â‡’ P(not E) = 1 âˆ’ 0.05

= 0.95

Thus, probability of â€˜not Eâ€™ = 0.95.

**Q 6. A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out (i) an orange flavoured candy? (ii) a lemon flavoured candy?**

âˆ´ Taking out any orange flavoured candy is not possible.

â‡’ Probability of taking out an orange flavoured candy = 0.

(ii) Also, probability of taking out a lemon flavoured candy = 1.

**Q 7. It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?****Sol.** âˆ´ Let the probability of 2 students having same birthday = P(SB) And the probability of 2 students not having the same birthday = P(nSB)

âˆ´ P(SB) + P(nSB)=1

â‡’ P(SB) + 0.992 = 1

â‡’ P(SB)=1 âˆ’ 0.992 = 0.008

So, the required probability of 2 boys having the same birthday = **0.008.**

**Q 8. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red? (ii) not red?****Sol.** Total number of balls = 3 + 5 = 8

âˆ´ Number of all possible outcomes = 8**(i) For red balls:** a There are 3 red balls.

âˆ´ Number of favourable outcomes = 3

= 3/8**(ii) For not red balls: **

Probability of the ball drawn which is not red

**Q 9. A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red? and (ii) white? (iii) not green?****Sol.** Total number of marbles = 5 + 8 + 4 = 17**(i) For red marbles:**

âˆµ Number of red marbles = 5

âˆ´ Number of favourable outcomes = 5

âˆ´ Probability of red marbles, P(red) = 5/17**(ii) For white balls:**

a Number of white balls = 8

âˆ´ Probability of white balls,

P(white)= 8/17**(iii) For not green balls: **

âˆµ Number of white balls = 4

âˆ´ Number of â€˜not greenâ€™ balls = 17 âˆ’ 4 = 13

i.e., Favourable outcomes = 13

P(not green) = 13/17

OR

Number of green marbles = 4

âˆ´ Number of â€˜not green ballsâ€™ = 17 âˆ’ 4 = 13

â‡’ Favourable outcomes = 13

âˆ´ P(not green) = 13/17

**Q 10. A piggy bank contains hundred 50p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin (i) will be a 50p coin? and (ii) will not be Rs 5 coin?****Sol. **Number of:

50 p coins = 100

Re 1 coins = 50

Rs 2 coins = 20

Rs 5 coins = 10

Total number of coins = 100 + 50 + 20 + 5 = 180

(i) For a 50 p coin:

Favourable events = 100

âˆ´ P(50 p) = 100/180 = 5/9

(ii) For not a Rs 5 coin:

a Number of Rs 5 coins = 10

âˆ´ Number of â€˜not Rs 5â€™ coins = 180 âˆ’ 10 = 170

â‡’ Favourable outcomes = 170

âˆ´ P(not 5 rupee coin) = 170/180 = 17/18.

**Q 11. Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see Fig.). What is the probability that the fish taken out is a male fish?**

**Sol.** Number of:

Male fishes = 5

Female fishes = 8

âˆ´ Total number of fishes = 5 + 8 = 13

â‡’ Total number of outcomes = 13

For a male fish:

Number of favourable outcomes = 5

âˆ´ P(male fish) = 5/13.

**Q 12. A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see figure), and these are equally likely outcomes. What is the probability that it will point at ****(i) 8 ?(ii) an odd number?(iii) a number greater than 2?(iv) a number less than 9?**

Total number of outcomes = 8

Number of favourable outcomes = 1

= 1/8

Number of odd numbers from 1 to 8 = 4

[âˆµ Odd numbers are 1, 3, 5 and 7]

â‡’ Number of favourable outcomes = 4

Number of numbers greater than 2 = 6

[âˆ´ The numbers 2, 3, 4, 5, 6, 7 and 8 are greater than 2]

â‡’ Number of favourable outcomes = 6

Number of numbers less than 9 = 8

[a The numbers 1, 2, 3, 4, 5, 6, 7 and 8 are less than 9]

âˆ´ Number of favourable outcome = 8

**Q 13. A die is thrown once. Find the probability of getting: (i) a prime number; (ii) a number lying between 2 and 6; (iii) an odd number.**

âˆ´ Number of total outcomes = 6

Since 2, 3, and 5 are prime number,

âˆ´ Favourable outcomes = 3

Since the numbers between 2 and 6 are 3, 4 and 5

âˆ´ Favourable outcomes = 3

Since 1, 3 and 5 are odd numbers.

â‡’ Favourable outcomes = 3

**Q 14. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting: (i) a king of red colour (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) the queen of diamonds **

âˆ´ Total number of possible outcomes = 52

âˆµ Number of red colour kings = 2

[âˆµ Kings of diamond and heart are red]

âˆ´ Number of favourable outcomes = 2

âˆµ 4 kings, 4 queens and 4 jacks are face cards

âˆ´ Number of face cards = 12

â‡’ Number of favourable outcomes = 12

Since, cards of diamond and heart are red

âˆ´ There are [2 kings, 2 queens, 2 jacks] 6 cards are red

â‡’ Favourable outcomes = 6

Since, there is only 1 jack of hearts.

âˆ´ Number of favourable outcomes = 1

âˆµThere are 13 spades in a pack of 52 cards:

âˆ´ Favourable outcomes are 13.

âˆµ There is only one queen of diamond.

âˆ´ Number of favourable outcomes.

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