What is the probability of getting exactly three heads on

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

BTGmoderatorLU wrote:Source: Veritas Prep

What is the probability of getting three heads on five flips of a fair coin?

A. 1/32
B. 3/32
C. 1/4
D. 5/16
E. 1/2

We first need to determine the probability of:

HHHTT

Since the probability of heads is 1/2 and the probability of tails is also 1/2 , we initially have (1/2)^5 = 1/32 as the probability of HHHTT.

We can order HHHTT in 5!/(3! x 2!) = 5 x 2 = 10 ways, using the indistinguishable permutations formula.
Thus, the probability of getting three heads in five flips of a fair coin is 10/32 = 5/16.

Answer: D