"This season, the probability that the Yankees will win a game is $0.49$ and the probability that the Yankees will score 5 or more runs in a game is $0.62$. The probability that the Yankees win and score 5 or more runs is $0.42$."
Shouldn't the probability be $0.49*0.62=0.30$? How can they say that the answer is .42?
Also, shouldn't the $P(B)$ cancel out with the numerator in the above theorem.
Multiplying the two probabilities only works if the two events are independent of one another. For example, the odds that two dice rolled separately will both be 6 is $\frac{1}{6}*\frac{1}{6}=\frac{1}{36}$. The two events in your problem are not independent. A team is significantly more likely to win if they have scored 5 or more runs. This is similar to calculating the probability that a die will roll an even number above three. The probability of rolling an even number is $\frac{1}{2}$, and the probability of rolling a number above 3 is also $\frac{1}{2}$. But this doesn't mean that the odds of rolling an even number above three is $\frac{1}{4}$. We can count the cases and see the the probability is $\frac{2}{6}$ or $\frac{1}{3}$. The discrepancy between the $0.30$ that you calculated and the $0.42$ that is cited in the problem represents the effect that score lots of runs has on the probability of winning a game.