Symbolic probability rules

Question

Given P(A)=0.24, P(B)=0.4 and P(A or B)=0.464, find the value of P(A and B), rounding to the nearest thousandth, if necessary.

Answer 1

P(A or B)=P(A)+P(B)-P(A and B) We substitute

Thus 0.464=0.24+0.4-P(A and B) add terms on right side

0.464=0.64-P(A and B) subtract so that -P(A and B) is by itself

-0.176=-P(A and B) switch terms and divide both sides by -1

P(A and B) = 0.176