Question

A bag contains 10 white and 3 red balls while another bag contains 3 white balls 5 red balls, 2 balls are drawn at random from the second bag. What is he probability that it is white ball?

Answer 1

Answer:

0.4538

Step-by-step explanation:

Let EWW be the event that two balls drawn from the first bag are both white. Likewise, EWR be the event that one white ball and one red ball are drawn from the first bag, and ERR be the event that two balls drawn from the first bag are both red. Let W be the event that a white ball is drawn from the second bag.

By Law of total probability,

Pr(W)=====≈Pr(EWW)Pr(W|EWW)+Pr(EWR)Pr(W|EWR)+Pr(ERR)Pr(W|ERR)(102)(132)×510+(101)(31)(132)×410+(32)(132)×3104578×510+3078×410+378×31035478059130

0.4538