Question

The Venn Diagram shows a universe with 26 elements and two different outcomes: B and Y

Answer 1

1. B and Y are 2 events,and Y has already occurred.  

2. P(B|Y)=P(B∩Y)/P(Y),

gives the probability of B to occur, once Y has already happened. 

3. According to the givens (check the diagram at the bottom, of the described problem), 

P(B∩Y)=n(B∩Y)/n(U)=8/26=4/13

P(Y)=n(Y)/n(U)=12/26=6/13

P(B|Y)=P(B∩Y)/P(Y)=(4/13)/(6/13)=4/6=2/3=0.67

Answer 2

Answer with explanation:

Universal set =U=26

B=8

Y=12

B ∩ Y=8

Probability of an event is defined as total favorable outcome divided by total possible outcome.

$P(B)=\frac{8}{26}\\\\P(Y)=\frac{12}{26}\\\\ P(B\cap Y)=\frac{8}{26}$

$P(\frac{B}{Y})=\frac{P(B\cap Y)}{P(Y)}\\\\P(\frac{B}{Y})=\frac{\frac{8}{26}}{\frac{12}{26}}\\\\P(\frac{B}{Y})=\frac{8}{12}\\\\P(\frac{B}{Y})=\frac{2}{3}$

 =0.666.....

=0.67 (approx)→→Required probability