SOLUTION: The probability of rain is 0.1. The probability of sun is 0.8, and the probability of a sun shower is 0.02. What is the probability of either rain or sun but not both? a) 0.76

Algebra ->  Probability-and-statistics -> SOLUTION: The probability of rain is 0.1. The probability of sun is 0.8, and the probability of a sun shower is 0.02. What is the probability of either rain or sun but not both? a) 0.76       Log On


   



Question 1190229: The probability of rain is 0.1. The probability of sun is 0.8,
and the probability of a sun shower is 0.02. What is the
probability of either rain or sun but not both?
a) 0.76
b) 0.91
c) 0.88
d) 0.96
e) 0.81

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Define these two event labels:
A = event of rain
B = event of sun

Given:
P(A) = 0.1
P(B) = 0.8
P(A and B) = 0.02

Based on those values, we can then say,
P(A or B, not both) = P(A) + P(B) - 2*P(A and B)
P(A or B, not both) = 0.1 + 0.8 - 2*0.02
P(A or B, not both) = 0.86

Unfortunately this answer choice is not listed.
Your teacher might have made a typo somewhere in generating the answer choices.

It's also quite possible I made an error somewhere. If so, then I apologize and I'll let another tutor offer a second opinion.

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It's a bit curious how
P(A or B, or both) = P(A) + P(B) - P(A and B)
P(A or B, or both) = 0.1 + 0.8 - 0.02
P(A or B, or both) = 0.88
does match up with choice C, so perhaps that's what your teacher was aiming for.