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

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) (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.

-------------

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.

RELATED QUESTIONS
the orbit of mercury around the sun forms an ellipse with eccentricity 0.206,length of... (answered by Alan3354)

The probability of rain on Monday is 0.1. The probability of rain on Tuesday is 0.8. What (answered by stanbon)

Suppose the probability of rain on Saturday is 25% and the probability of rain on Sunday... (answered by richard1234)

Venus Orbit Problem Venus orbits the sun in an approximately circular path. Venus is... (answered by ElectricPavlov)

The probability of passing exam is 0.8, what is the probability of failing... (answered by ikleyn)

Probability Topics and Discrete Probability Distributions: Suppose the weatherman... (answered by Fombitz)

There is an x chance of rain tomorrow. What is the probability of no rain tomorrow? (answered by ikleyn)

during the cold season,the sun is visible 25% of the time .The probability that the class (answered by Boreal)

Please help me to solve this question. During the cold season the sun is visible 25% of... (answered by Boreal)