Mathematics

Problem

For three events

A

B

and

C

in a sample space, the following probabilities are known:

P(A)=0.6,\;P(B)=0.5,\;P(C)=0.4,

P(A\cap B)=0.3,\;P(A\cap C)=0.24,\;P(B\cap C)=0.2,

P(A\cap B\cap C)=0.12.

Calculate

P\bigl(A\mid (B\cap C)\bigr)