Question

Let U1 , and U2 , be two urns such that U1 , contains 3 white and 2 red balls, and U2, contains only1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U1 , and put into U2, . However, if tail appears then 2 balls are drawn at random from U1, and put into U2 . . Now 1 ball is drawn at random from U2, .61 . The probability of the drawn ball from U2, being white is A. 13 30 B. 23 30 C. 19 30 D. 11 30 Select the correct answer from above options

Answer 1

Correct Answer - D By total probability theorem Required probability = 1 2 × ( 3 5 × 1 + 2 5 × 1 2 ) + 1 2 ( . 3 C 2 . 5 C 2 × 1 + . 2 C 2 . 5 C 2 × 1 + . 2 C 2 . 5 C 2 × 1 3 + . 3 C 1 × . 2 C 1 . 5 C 2 × 2 3 ) = 23 30