Question

There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white is

Solution

Correct option is

2/3

Let Ei (0 ≤ i ≤ 2) denote the vent that urn contains i white and (2 – i) black balls. Let A denote the event that a white ball is drawn from the urn.

We have    P(Ei) = 1/3      for     i = 0, 1, 2 and

     

By the total probability rule,

       

                 

SIMILAR QUESTIONS

Q1

If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that two white and one black ball will be drawn is

Q2

There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is

Q3

A group of 2n boys and 2n girls is randomly divided into two equal groups. The probability that each group contains the same number of boys and girls is

Q4

Let A and B be two events such that P(A) = 0.3 and P(A  B) = 0.8. If Aand B are independent events, then P(B) is

Q5

An unbiased dia with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times out of the four faces obtained, the probability that the minimum value is exactly than 2 and the maximum value is exactly 5 is

Q6

A pair of unbiased dice is rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is

Q7

Each of two persons A and B toss three fair coins. The probability that both get the same number of heads is

Q8

The probability that a student is not a swimmer is 1/5. The probability that out of 5 students exactly 4 is swimmer is

Q9

Six distinct numbers are selected from first 150 natural numbers. The probability all the six numbers are divisible both by 3 and 5 is

Q10

A natural number x is chosen at random from the first one hundred natural numbers. The probability that   is