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

BTGmoderatorDC wrote: ↑

Mon Apr 06, 2020 5:35 pm

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

Source: Veritas Prep

For a fair coin, the probability of getting a head or a tail = 1/2

She can get at least one head and one tail in the following ways: 1 head, 4 tails; 2 heads, 3 tails;3 heads, 2 tails;4 heads, 1 tail.

• Probability of getting 1 head and 4 tails = 5C1*(1/2)*(1/2)^4 = 5/32;
• Probability of getting 2 heads and 3 tails = 5C2*(1/2)^2*(1/2)^3 = 10/32;
• Probability of getting 3 heads and 2 tails = 5C3*(1/2)^3*(1/2)^2 = 10/32;
• Probability of getting 4 heads and 1 tail = 5C4*(1/2)^4*(1/2) = 5/32

So, the probability that she will receive at least one head and one tail
= 5/32 + 10/32 + 10/32 + 5/32 = 30/32 = 15/16

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC wrote: ↑

Mon Apr 06, 2020 5:35 pm

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

Source: Veritas Prep

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

BTGmoderatorDC wrote: ↑

Mon Apr 06, 2020 5:35 pm

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

Source: Veritas Prep

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 to 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