In a recent survey of residents in the Degobah system 10 of

In a recent survey of residents in the Degobah system, 10% of the families have met a Wookie and 52% have met a Bantha. Of the homes that have met a Wookie, 91% also have met a Bantha. Given that a home has met a Bantha, what is the probability that they have also met a Wookie?

I\'m very confused with this question and would like to see if anyone can help provide clarity! Thank you

Solution

Sol)

Probability that families have met a Wookie P(A)= 10%

Probability that families have met a Bantha P(B) =52%

Probability that Of the homes that have met a Wookie, 91% also have met a Bantha P(B/A)=0.91

Now P(B/A) =P(A and B) / P(A)

0.91 = P(A and B) / 0.

P(A and B) =0.91*0.1

P(A and B) =0.091

Now Probability that a home has met a Bantha, what is the probability that they have also met a Wookie

P(A/B) = P(A and B) / P(B) = 0.091 / 0.52

P(A/B) =0.175