Please help I’ve tried and can not figure it out

let the probability of Aron going on Saturday be A

A

= {Aaron goes to the gym on Monday},

and the probability of him going on a Sunday be B

B

= {Aaron goes to the gym on Sunday}.

In your post, we have the following pieces of information:

P(A)=0.8

P(A)=0.8

,

P(B∣A)=0.3

P(B∣A)=0.3

,

P(B∣A)=0.9

P(B∣A¯)=0.9

.

What you are looking for is the probability that he goes only once (either on Saturday or Sunday). That is the probability of the event

(A∩B¯)∪(A¯∩B)

(A∩B¯)∪(A¯∩B)

. [(A∩B¯)(A∩B¯)

: if he goes on Saturday he won't go on Sunday

A¯∩B

A¯∩B

: if he did not go on Saturday, he will go on Sunday].

We have:

P

((A ∩B)∪(A∩B))

=

P(A∩B)+

P(A∩B)

=

P(B∣A)

P(A)+

P(B∣A)

P(A)

=

(1−P(B∣A))

P(A)

+

P(B∣A)

(1−P(A))

=(1−0.3)×0.8+0.9×0.2

The prob of Aaron going to the gym on exactly one of the two days is =0.74.

P((A∩B¯)∪(A¯∩B))=P(A∩B¯)+P(A¯∩B)=P(B¯)

the aswere is the one with all 8's and the second one is with the 10,8 and 6

step-by-step explanation: