Problem Solving

AAPL wrote:Veritas Prep

If a child flips a coin five times in a row, what is the probability that she will receive at least one head and one tail?

A. 3/4
B. 11/12
C. 15/16
D. 31/32
E. 63/64

OA C

If a coin is flipped 5 times in a row, there are 32 possible outcomes (HHTTH, HTHTT, TTTTT, etc)
How did we get 32?
Well, there are 2 possible outcomes for the 1st coin flip, 2 possible outcomes for the 2nd coin flip, 2 outcomes for the 3rd flip, 2 outcomes for the 4th flip, and 2 outcomes for the 5th flip,
By the Fundamental Counting Principle (FCP), the TOTAL number of outcomes when flipping 5 coins = (2)(2)(2)(2)(2) = 32

Of course, among those 32 outcomes, there are some outcomes that DO NOT meeting the required condition that we receive at least one head and one tail
There are EXACTLY 2 outcomes that DO NOT meet this required condition.
They are: TTTTT and HHHHH

So, the number of outcomes that DO meet the required condition = 32 - 2 = 30

So, P(child gets at least one head and one tail) = 30/32= 15/16

Answer: C

Cheers,
Brent

AAPL wrote:Veritas Prep

If a child flips a coin five times in a row, what is the probability that she will receive at least one head and one tail?

A. 3/4
B. 11/12
C. 15/16
D. 31/32
E. 63/64

Since each coin has two faces, head and tail, there are 2^5 = 32 different combinations when flipping a coin five times in a row. Of these 32 combinations, only two of them do not have at least one head and one tail. It occurs when all 5 flips turn out to be heads (HHHHH) or all 5 turn out the be tails (TTTTT). The other 30 combinations will have at least one head and one tail, so the probability is 30/32 = 15/16.

Answer: C