Question

On any particular Saturday evening, the probability that Jenna will go to the movies and go for coffee is start fraction one over five end fraction full stop The probability that she will go for coffee, given that she has gone to the movies, is start fraction seven over eight end fraction. What is the probability that Jenna will go to the movies on any particular Saturday?

start fraction 8 over 35 end fraction
start fraction 7 over 40 end fraction
start fraction 1 over 40 end fraction
start fraction 7 over 12 end fraction

Answer 1

start fraction 8 over 35 end fraction

Explanation:

Let M represent Movies and C represent Coffee

The Probability that Jenna will go to the movies and go for coffee is

P ( M $ C) =
`(1)/(5)`

P ( M ║ C ) =
`(7)/(8)`

P (M) = ???

∴

P ( M $ C) = P (M) × P ( M ║ C )

`(1)/(5)` = P (M) ×
`(7)/(8)`

`(1)/(5)` ÷
`(7)/(8)` = P (M)

`(1)/(5) *(8)/(7) = P (M)`

P (M) =
`(8)/(35)`

Hence, the probability that Jenna will go to the movies on any particular Saturday P (M) =
`(8)/(35)`