Question

consider a sample space defined by events a1, a2, b1 and b2 where a1 and a2 are complements .given p(a1)=0.2 p(b1/a1) = 0.5 and p(b1/a2) =0.7 what is the probability of p (a1/b1)

P(A1/B1)=

round to the 3rd decimal

Answer 1

The conditional probability formula

Therefore using the conditional probability rule

= 0.5 * 0.2

Similarly

But we need to find first . We know that a1 and a2 are complements therefore

=1 - 0.2

= 0.8

= 0.7*0.8

This is because we add all possible combinations of b1 which gives its probability.

= 0.10 + 0.56

= 0.10 / 0.66