The probability that Serena does not serve an ace or a double fault is 0.63..
Addition rule of probability applies to the calculation of probability for one or another event happen. These events are either mutually exclusive or not .
We have following information,
The probability of Serena serving an ace in tennis (p) = 0.15
Probability that she double faults(q) = 0.25
The probability of Serena not serving an ace in tennis = 1 -p = 1 - 0.15 = 0.85
let A and B be two events Serena not serving an ace and she double faults respectively.
Events A and B are not mutually exclusive events .
i.e, P(A ∩ B ) =/ 0
when Serna not serving an ace implies that either it is double faults or not and both have equally likely chance.
So, the probability of intersection of event A and B = 0.85/2 = 0.47
Adding Rule for probabilities is
P(A or B ) = P(A) + P(B) - P(A ∩ B)
The probability that Serena does not serve an ace or a double fault = 0.85 + 0.25 - 0.47
= 1.10 - 0.47 = 0.63...
Hence, the probability that Serena does not serve an ace or double fault is 0.63..
To learn more about Probability, refer:
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