Question

Suppose A and B are independent events with $P\left(A\right)=0.6,P\left(B\right)=0.7$.Then compute:

a)$P(A\bigcap B)$

b) $P(A\bigcup B)$

c)$P\left(B/A\right)$

d) $P(A^c\bigcap B^c)$

Answer 1

Given,

$P\left(A\right)=0.6,P\left(B\right)=0.7$

Since these are independent event,

So,

a). $P(A\cap B)=P\left(A\right).P\left(B\right)=0.6\times 0.7=0.42$

b). $P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)=0.7+0.6-0.42=0.88$

c). $P\left(B/A\right)=\frac{P(A\cap B)}{P\left(A\right)}=\frac{0.42}{0.6}=0.7$

d). $P(A^c\cap B^c)=1-P(A\cup B)=1-0.88=0.12$