Question:
Let A and B be two events associated with a random experiment for which P(A) = 0.4, P(B) = 0.5 and P(A or B) = 0.6. Find P(A and B).
Solution:
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 $\mathrm{B})=0.3$