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The probability that a consumer testing service will rate a new antipollution device for cars very poor, poor, fair, good, very good, or excellent are $0.07,0.12,0.17,0.32$, $0.21$, and $0.11$. What are the probabilities that it will rate the device

(a) very poor, poor, fair, or good;

(b) good, very good, or excellent?
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Since the probabilities are all mutually exclusive, direct substitution into the formula $P\left(A_{1} \cup A_{2} \cup \cdots \cup A_{n}\right)=P\left(A_{1}\right)+P\left(A_{2}\right)+\cdots+P\left(A_{n}\right)$ yields
$0.07+0.12+0.17+0.32=0.68$
for part (a) and
$0.32+0.21+0.11=0.64$
for part (b)
by Diamond (40,719 points)

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