What is the probability of getting only one head in a single throw

Question

What is the probability of getting only 1 head in a single throw of three fair coins?

A) 1/2
B) 3/8
C) 1/4
D) 1/5
E) 5/8

Source: 4gmat

How do we solve such problems?

Ashishmathew01081987 · Answer

I'm a bit confused with the wording in the question and the answer choices. I was wondering if you meant probability of getting only 1 head.

According to the way the question is answer should be 7/8
If the question is of getting only one head then answer is 3/8

Explanation

Probability of an event = No. of ways in which event occurs / Total number of outcomes possible

On tossing three coins the total number of outcomes possible are

HHH
HHT
HTH
THH
HTT
THT
TTH
TTT

So there are 8 possible outcomes. Now to find the probability of desired outcomes.

Case I :
Probability of getting a head ( Can be only 1 head, 2 Heads or 3 Heads)

HHH
HHT
HTH
THH
HTT
THT
TTH

So 7 ways in which event occurs out of 8 possible outcomes. Hence probability = 7/8

Case II:
Probability of getting "ONLY" one head

HTT
THT
TTH

So 3 ways in which event occurs out of 8 possible outcomes. Hence probability = 3/8

I guess your question should have been to find the probability of getting ONLY one head, then the answer is B

alphonsa · Answer

Thanks. I had posted the question the way it had been worded in the book

However to avoid confusion, I have edited it here

JeffTargetTestPrep · Answer

We need to determine the probability of H-T-T = 1/2 x 1/2 x 1/2 = 1/8.

Since H-T-T can be arranged in 3!/2! = 3 ways, the total probability is 3/8.

Answer: B

CrackverbalGMAT · Answer

The question in itself is pretty simple. When it says only 1 head, it means exactly 1 head (the other ways it would have been worded are at least one head or at most one head).

Probability = \frac{Favorable \space Outcomes}{Total \space Outcomes}

When throwing three coins the total outcomes =  2^3 = 8

Favorable outcomes = Getting 1 head on any of the 3 coins =  ^3C_1 = 3

The required Probability = 3/8

Option B

Arun Kumar

What is the probability of getting only one head in a single throw

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