Question

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

B=8
Y=12
Both=8
Find the following probability and write your answer as a decimal:

P(B|Y) =

Answer 1

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)=(8)/(26)\\\\P(Y)=(12)/(26)\\\\ P(B\cap Y)=(8)/(26)`

`P((B)/(Y))=(P(B\cap Y))/(P(Y))\\\\P((B)/(Y))=((8)/(26))/((12)/(26))\\\\P((B)/(Y))=(8)/(12)\\\\P((B)/(Y))=(2)/(3)`

=0.666.....

=0.67 (approx)→→Required probability

Answer 2

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