by jen Fri Sep 30, 2011 3:50 pm
Hi Docsomi,
What a strange little question. I don't think it's very GRE-like, because a GRE question probably wouldn't ask "What is the probability that ///at least one/// of them wins the prize?" if there's only one prize.
That said, the rule is that "AND" problems mean that you multiply, and "OR" problems in which the events are mutually exclusive mean that you add. Here, it's just 0.4 + 0.5 = 0.9.
But let's think about some other scenarios!
What if there were multiple prizes, and Tom still had a 0.5 chance and John a 0.4 chance? THEN, we would multiply to get the chance that BOTH will win (0.2).
What if there were multiple prizes, but we still wanted the probability that AT LEAST one of them would win? Then we couldn't just add 0.4 + 0.5, because we'd be double-counting the scenario in which both men win. There are a few ways to solve this, but the easiest one would be to calculate the probability that neither wins, and subtract from 1. So, 0.6 times 0.5 = 0.3, the probability that neither wins. Subtract 1 - 0.3 to get 0.7, the probability that at least one wins (if more than one prize exists).
Anyway, those were some side issues there -- the problem as posted is pretty simple!
Jen