Hi All,
We're asked for the probability of getting EXACTLY three heads on five flips of a fair coin. This question can be approached in a couple of different ways, but they all involve a bit of 'Probability math.'
To start, since each coin has two possible outcomes, there are (2)(2)(2)(2)(2) = 32 possible outcomes from flipping 5 coins. To find the number of outcomes that are EXACTLY 3 heads, you can either use the Combination Formula or do some 'brute force' math and map out all of the possibilities.
By choosing 3 heads from 5 tosses, we can use the Combination Formula: N!/(K!)(N-K)! = 5!/(3!)(5-3)! = (5)(4)(3)(2)(1)/(3)(2)(1)(2)(1) = (5)(4)/(2)(1) = 10 possible ways to flip 3 heads from 5 tosses.
You could also list out the options:
HHHTT
HHTHT
HTHHT
THHHT
HHTTH
HTHTH
THHTH
HTTHH
THTHH
TTHHH
Either way, you have 10 total options that fit what we're looking for out of a total of 32 outcomes. 10/32 = 5/16
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
