Questions about the world of GRE Math from other sources and general math related questions.
docsomi
Students
 
Posts: 1
Joined: Tue Sep 06, 2011 4:04 am
 

Help with a Math question please

by docsomi Tue Sep 20, 2011 9:20 pm

The probability that Tom will win the Booker prize is 0.5, and the probability that John will win the Booker prize is 0.4. There is only one Booker prize to win. What is the probability that at least one of them wins the prize?
(A) 0.2
(B) 0.4
(C) 0.7
(D) 0.8
(E) 0.9

Can you please help me work out this problem with explanation regarding the events being mutually exclusive & independent? Thank you!
jen
Manhattan Prep Staff
 
Posts: 51
Joined: Mon Mar 28, 2011 9:50 am
 

Re: Help with a Math question please

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