Test: Probability And Expected Value By Mathematical Expectation- 3 - CA Foundation MCQ

There are three boxes with the following composition:

Box I: 5 Red + 7 White + 6 Blue balls

Box II: 4 Red + 8 White + 6 Blue balls

Box III: 3 Red + 4 White + 2 Blue balls

If one ball is drawn at random, then what is the probability that they would be of same colour?

A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11?

A bag contains 8 red and 5 white balls. Two successive draws of 3 balls are made without replacement. The probability that the first draw will produce 3 white balls and the second 3 red balls is

There are two boxes containing 5 white and 6 blue balls and 3 white and 7 blue balls respectively. If one of the the boxes is selected at random and a ball is drawn from it, then the probability that the ball is blue is

A problem in probability was given to three CA students A, B and C whose chances of solving it are 1/3, 1/5 and 1/2 respectively. What is the probability that the problem would be solved?

There are three persons aged 60, 65 and 70 years old. The survivals probabilities for these three persons for another 5 years are 0.7, 0.4 and 0.2 respectively. What is the probability that at least two of them would survive another five years?

​Tom speaks truth in 30 percent cases and Dick speaks truth in 25 percent cases. What is the probability that they would contradict each other?

There are two urns. The first urn contains 3 red and 5 white balls whereas the second urn contains 4 red and 6 white balls. A ball is taken at random from the first urn and is transferred to the second urn. Now another ball is selected at random from the second arm. The probability that the second ball would be red is

For a group of students, 30 %, 40% and 50% failed in Physics , Chemistry and at least one of the two subjects respectively. If an examinee is selected at random, what is the probability that he passed in Physics if it is known that he failed in Chemistry?

A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective?

8 identical balls are placed at random in three bags. What is the probability that the first bag will contain 3 balls?

X and Y stand in a line with 6 other people. What is the probability that there are 3 persons between them?

Given that P (A) = 1/2, P (B) = 1/3, P (A ∩ B) = 1/4, what is P (A’/B’)

Four digits 1, 2, 4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4?

The probability distribution of a random variable x is given below:

Q. What is the standard deviation of x? 

A packet of 10 electronic components is known to include 3 defectives. If 4 components are selected from the packet at random, what is the expected value of the number of defective?

The probability that there is at least one error in an account statement prepared by 3 persons A, B and C are 0.2, 0.3 and 0.1 respectively. If A, B and C prepare 60, 70 and 90 such statements, then the expected number of correct statements

A bag contains 6 white and 4 red balls. If a person draws 2 balls and receives Rs.10 and Rs.20 for a white and red balls respectively, then his expected amount is

The probability distribution of a random variable is as follows:

Q. The variance of x is 

All possible outcomes of a random experiment forms the

If one of outcomes cannot be expected to occur in preference to the other in an experiment the events are

If two events cannot occur simultaneously in the same trial then they are

When the no. of cases favourable to the event A=0 then P(A) is equal to

A card is drawn from a well-shuffled pack of playing cards. The probability that it is a spade is

A card is drawn from a well-shuffled pack of playing cards. The probability that it is a king is

A card is drawn from a well-shuffled pack of playing cards. The probability that it is the ace of clubs is

In a single throw with two dice the probability of getting a sum of five on the two dice is