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Two persons are studying for a test.

X’s chances of getting a “B” are 80%. Y’s chances of getting a “B” are 90%.

The probability of at least one of them getting a “B” is 91%.

a. What is the probability that only X gets a “B”?

b. What is the probability that only Y gets a “B”?

c. What is the probability that both won’t get a “B”?

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Note that P(X gets B)+P(Y gets B)=P(at least one gets B)+P(X and Y gets B), so P(X ang Y gets B)=0.8+0.9-0.91=0.79.

Now:

a. P(only X gets B)=P(X gets B)-P(X and Y gets B)=0.8-0.79=0.01

b. P(only Y gets B)=P(Y gets B)-P(X and Y gets B)=0.9-0.79=0.11

c. P(both won't get B)=1-P(at least one gets B)=1-0.91=0.09

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    Note that we can't suppose that the events X gets B and Y gets B, are independent. – 2017-02-11