Question

For two events $A$ and $B,P\left(B\right)=P\left(B/A\right)=1/3$ and $P\left(A/B\right)=4/7,$ then
Option a : $P\left(B^{\prime }/A\right)=2/3$
Option b : $P\left(A/B^{\prime }\right)=3/7$
Option c : $A$ and $B$ are mutually exclusive
Option d: $A$ and $B$ are independent

• A. $a,c$
• B. $a,b,c$
• C. $b,c,d$
• D. $a,c,d$

Answer 1

The correct option is A $a,c$

$P\left(B\right)=P\left(B/A\right)=1/3$ $P\left(A/B\right)=4/7$

If $P\left(B\right)=P\left(B/A\right)$ then $A$ and $B$ are independent or mutually exclusive events

then $P\left(B\right)=1/3$ $P\left(A/B\right)=P\left(A\right)=4/7$

$P\left(B^1/A\right)=P\left(B^1\right)=1-1/3=2/3$

$P\left(A/B^1\right)=P\left(A\right)=4/7$