The probability that Aaron goes to the gym on Saturday is 0.8

If Aaron goes to the gym on Saturday the probability that he goes on Sunday is 0.3.

if Aaron does not go to the gym on Saturday the probability he goes on Sunday is 0.9.

Calculate the probability the Aaron goes to the gym on exactly one of the two days.

0.74

Step-by-step explanation:

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The probability that Aaron goes to the gym on exactly one of the two days is 0.74

Step-by-step explanation:

Let P (Aaron goes to the gym on exactly one of the two days) be the probability that Aaron goes to the gym on exactly one of the two days.

Then

P (Aaron goes to the gym on exactly one of the two days) =

P (Aaron goes to the gym on Saturday and doesn't go on Sunday) +

P (Aaron doesn't go to the gym on Saturday and goes on Sunday)

If Aaron goes to the gym on Saturday the probability that he goes on Sunday is 0.3. Then If Aaron goes to the gym on Saturday the probability that he does not go on Sunday is 1-0.3 = 0.7 Since the probability that Aaron goes to the gym on Saturday is 0.8,

P (Aaron goes to the gym on Saturday and doesn't go on Sunday) =

P (the probability that Aaron goes to the gym on Saturday) * P (If Aaron goes to the gym on Saturday the probability that he does not go on Sunday)

=0.8*0.7=0.56

The probability that Aaron doesn't go to the gym on Saturday is 1-0.8=0.2 And if Aaron does not go to the gym on Saturday the probability he goes on Sunday is 0.9.

Thus, P (Aaron doesn't go to the gym on Saturday and goes on Sunday) = P (The probability that Aaron doesn't go to the gym on Saturday) * P (if Aaron does not go to the gym on Saturday the probability he goes on Sunday)

=0.2*0.9=0.18

Then

P (Aaron goes to the gym on exactly one of the two days) = 0.56 + 0.18 = 0.74