Answer: a) 0.15
b) 0.300
Step-by-step 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 [tex]P(B|A)=\dfrac{P(A\cap B)}{P(A)}[/tex], we have
[tex]P(A\cap B)=P(B|A)\timesP(A)[/tex]
Similarly,
a) The probability that both John and Jane watch the show will be :-
[tex]\text{P(John}\cap \text{Jane)}=\text{P(John }|\text{ Jane)}\times\text{P(Jane)}\\\\=0.3\times0.5=0.15[/tex]
b) The probability that Jane watches the show, given that John does will be :-
[tex]\text{P(John }|\text{ Jane)}=\dfrac{\text{P(John}\cap \text{Jane)}}{\text{P(John)}}\\\\=\dfrac{0.15}{0.5}=0.3[/tex]
Hence, the probability that Jane watches the show, given that John does. = 0.300
