Question

According to the general equation for conditional probability, if p (a^b')=1/6 and p(b')=7/12 , what is the value of p(a[b)?

Answer 1

P(B) = 1 - P(B') = 1 - (7/12) = 5/12 P(A∩B)=P(A∩B′)/P(B′) × P(B)/1

Plugging values into the last equation we get: P(A∩B)=1×12×5 / 6×7×12 = 542
Now we can make use of the following formula P(A|B)=P(A∩B) / P(B) by plugging in the values that we have found.

5/42 is the numerator and the denominator is 5/12.

The bottom (denominator) is P(B) which equals 5/12. P(A|B)=5×12 / 42×5 = 6/210

6/210 = 2/7

p(a[b]) = 2/7