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Box-I has 8 red balls, 3 blue balls, and 5 green balls. Box-II contains 24 red balls, 9 blue balls, and 15 green balls. Box-III includes 1 blue ball, 12 green balls, and 3 yellow balls. Box-IV holds 10 green balls, 16 orange balls, and 6 white balls. A ball is picked randomly from Box-I, referred to as b. If b is red, a ball is randomly selected from Box-II. If b is blue, a ball is randomly drawn from Box-III. If b is green, a ball is randomly picked from Box-IV. What is the conditional probability that 'one of the selected balls is white,' given that 'at least one of the selected balls is green'?
- 15/256
- 3/16
- 5/52
- 1/8
Correct answer: 5/52
Solution
The conditional probability is calculated by considering the cases where at least one green ball is selected and then determining the likelihood of selecting a white ball. Using the total probability theorem and the given distributions, the probability simplifies to 5/52.
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