Question

John and Jane are married. The probability that John watches a certain television show is .5. The probability that Jane watches the show is .5. The probability that John watches the show, given that Jane does, is .3. (a) Find the probability that both John and Jane watch the show. (Round your answer to 2 decimal places.) (b) Find the probability that Jane watches the show, given that John does. (Round your answer to 3 decimal places.)

Answer 1

Answer: a) 0.15

b) 0.300

Explanation:

Given : The probability that John watches a certain television show : P(John)=0.5

The probability that Jane watches the show is : P(Jane)= 0.5.

The probability that John watches the show, given that Jane does

=P(John | Jane)=0 .3.

Using Condition probability formula
`P(B|A)=(P(A\cap B))/(P(A))`, we have

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

Similarly,

a) The probability that both John and Jane watch the show will be :-

`\text{P(John}\cap \text{Jane)}=\text{P(John }|\text{ Jane)}*\text{P(Jane)}\\\\=0.3*0.5=0.15`

b) The probability that Jane watches the show, given that John does will be :-

`\text{P(John }|\text{ Jane)}=\frac{\text{P(John}\cap \text{Jane)}}{\text{P(John)}}\\\\=(0.15)/(0.5)=0.3`

Hence, the probability that Jane watches the show, given that John does. = 0.300