Question

there are n bags such that i’th bag contains 1 black and 2 white balls.Two balls are drawn from a randomly selected bag out of n bags.fInd the probability that both balls drawn are white.

Answer 1

The probability that both balls drawn from a bag containing 1 black and 2 white balls are white is 1/3. This is calculated using combinations to find the successful and total outcomes of drawing 2 balls from the bag.

Step-by-step explanation:

The question asks for the probability of drawing two white balls from a bag containing 1 black and 2 white balls. To find this probability, we use the principles of combinatorics and probability.

First, calculate the number of ways to choose 2 white balls from the 2 white balls available, which is given by the combination formula C(n, k) = n! / (k! * (n-k)!), where 'n' is the total number of items to choose from, and 'k' is the number of items to choose. Thus:

• C(2, 2) = 2! / (2! * (2-2)!) = 1

Then, calculate the total number of ways to draw 2 balls out of the 3 (1 black and 2 white). This also follows the combination formula:

• C(3, 2) = 3! / (2! * (3-2)!) = 3

The probability is then the number of successful outcomes over the total number of outcomes, hence:

• P(both white) = Number of ways to choose 2 white balls / Total ways to choose 2 balls = 1 / 3

Therefore, the probability that both balls drawn are white is 1/3.