Let A and B be two events associated with a random experiment

Given : P(A) = 0.4, P(A or B) = 0.6 and P(B) = 0.5

To find : P(A and B)

Formula used : P(A or B) = P(A) + P(B) - P(A and B)

Substituting in the above formula we get

$0.6=0.4+0.5-P(A$ and $B)$

$0.6=0.9-\mathrm{P}(\mathrm{A}$ and $\mathrm{B})$

$P(A$ and $B)=0.9-0.6$

$P(A$ and $B)=0.3$

$\mathrm{P}(\mathrm{A}$ and $\mathrm{B})=0.3$