Question

Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls.  One ball is transferred from Bag I to Bag II and then two balls are drawn at  random (without replacement) from Bag II. The balls so drawn are found to be  both red in colour. Find the probability that the transferred ball is red.  Please answer this.​

Answer 1

Answer:

5/9

Step-by-step explanation:

Given:

Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then two balls are drawn at random (without replacement) from Bag II. The balls so drawn are found to be both red in colour. Find the probability that the transferred ball is red.​

Solution:

Let E1 : transferred ball is red.

E2 : transferred ball is black.

A : Getting both red from 2nd bag (after transfer)

P(E1)=3/7,P(E2)=4/7

P(A/E1) = 5c2/10c2=2/9

,P(A/E2) = 4c2/10c2=2/15

P(E1/A) = ((P(E1) P(A|E1))/ P(E1)P(A|E1)+P(E2)P(A|E2)

= 5/9