Question

A poll was conducted in states A, B, and C to determine which candidate voters would most likely vote for. The results are displayed in the table below: State A State B State C Total Liberal 20 21 12 53 Conservative 20 14 13 47 Total 40 35 25 100 What is P(liberal | State B)?

Answer 1

P(liberal | State A) means that probability of liberal candidates to be voted for within state A. This probability could be calculated by the pattern: number of successful events/total events. The successful events referred here is the number of liberal votes in state A. That is equal to 22. The total events is the total number of votes in state A which is 40.

The probability is 22/40 = 0.55

Answer 2

Answer:
`(3)/(5)`

Explanation:

The given table :

State A State B State C Total

Liberal 20 21 12 53

Conservative 20 14 13 47

Total 40 35 25 100

Since , the conditional probability of event A given B is given by :-

`P(A|B)=(P(A\cap B))/(P(B))`

Now,
`\text{P(State B)}=(35)/(100)`

`\text{P(liberal}\cap\text{State B)}=(21)/(100)`

Now,
`\text{P(liberal}|\text{State B)}=\frac{\text{P(liberal}\cap\text{State B)}}{\text{P(State B)}}`

`=((21)/(100))/((35)/(100))\\\\\\=(21)/(35)=(3)/(5)`