Question

An urn contains five balls. Two balls are drawn and found to be white. The probability that all the balls are white is:

• A. \( \frac{1}{10} \)
• B. \( \frac{3}{10} \)
• C. \( \frac{3}{5} \)
• D. \( \frac{1}{2} \)

Hint:

Use conditional probability to determine the likelihood of a specific event occurring given prior events.

Answer 1

The Correct Option is D

Step 1: There are 5 balls in total. Two balls are drawn and found to be white. The total number of ways to choose 2 balls from 5 is: \[ \binom{5}{2} = 10. \] Step 2: If all balls are white, there are only 3 white balls in the urn. The number of ways to choose 2 white balls from 3 is: \[ \binom{3}{2} = 3. \] Step 3: The probability that all the balls are white, given that two white balls were drawn, is: \[ P({All white}) = \frac{3}{6} = \frac{1}{2}. \] Thus, the probability that all the balls are white is \( \frac{1}{2} \).