##### Baye's Theorem Example 1

Bag A contains 3 red balls and 4 black balls while Bag B contains 5 red balls and 6 black balls.

One ball is drawn and it is found to be red. Find the probability that it was drawn from bag 'B' .

**Answer**

Solution:

P(B/R) = ??

we know P(B/R) = P(B∩R) / P(R).....(1)

and P(R/B) = P(B∩R) / P(B)......(2)

by using equation 2 we can say tha

P(B/R) ={ P(B). P(R/B) } / P(R)

and we alreday know how to calculate P(R) .

P(R)= P(B).(R/B) + P(A).P(R/B)

={(1/2).(5/11) +(1/2).(3/7) }

now

**P(B/R)= { (1/2).(5/11) } / {(1/2).(5/11) +(1/2).(3/7) } **