Respuesta :
a) The probability that both John and Jane watch the show is 0.12.
b.The probability that Jane watches the show, given that John does is 0.1714.
c)They do watch show independent of each other.
Step-by-step explanation:
Here, as given in the question:
Probability that John watches a certain show = 0.7 ⇒ P(J) = 0.7
Probability that Jane watches a certain show = 0.3 ⇒ P(Je) = 0.3
Probability that John watches a certain show given Jane watches it to
= 0.4 ⇒ P(J/Je) = 0.4
a. ) Here, we need to find the probability of both Jane and John watching a show , P(J∩Je)
Now, by BAYES THEOREM:
[tex]P(J/Je) = \frac{P(J \cap Je)}{P(Je)}[/tex]
[tex]\implies 0.4 = \frac{P(J \cap Je)}{0.3} \\\implies P(J \cap Je) = 0.4 \times 0.3 = 0.12[/tex]
Hence the probability that both John and Jane watch the show is 0.12.
b.) The probability that Jane watches the show, given that John does is P(J/Je)
By BAYES Theorem:
[tex]P(Je/J) = \frac{P(J \cap Je)}{P(J)}\\\implies P(Je/J) = \frac{0.12}{0.7} = 0.1714[/tex]
Hence, the probability that Jane watches the show, given that John does is 0.1714.
c) As we can see P(Jane ∩ John) = 0.12
So, the probability of both of them seeing the show TOGETHER is 0.12.
Hence, they do watch show independent of each other and the probability of doing that is 1.0.12 = 0.88
