John flips a coin 4 times. What is the probability that he gets heads

Question

John flips a coin 4 times. What is the probability that he gets heads on at least one of the four flips?

(A) 1/16
(B) 1/4
(C) 1/2
(D) 3/4
(E) 15/16

dina98 · Answer

Yes, E is correct. 
The probability of getting a heads at least once = 1 - probability of getting tails all 4 times.
Ans = 1 - (1/2)(1/2)(1/2)(1/2) = 1 - (1/16) = 15/16

mehtakaustubh · Answer

Total number of ways =2*2*2*2=16
Number of ways of not getting a single head..1
in all 16 possibilities there is only one in whcih we can get all tails
so probability of not getting a single head=1/16
now probability of getting atleast one head is 1-probability of not getting a single head
=1-1/16=15/16
Hope this helps..

DmitryFarberMPrep · Answer

The "1-x" short cut above is best here, but you can verify the long way.

There are 16 possible combinations here. They break down as follows:

1H, 3T: 4 ways (heads first, second, third, or fourth)
2H, 2T: 6 ways (heads in 1&2, 1&3, 1&4, 2&3, 2&4, or 3&4)
3H, 1T: 4 ways (as in the first one, but this time tails first, second, third, or fourth)
4H, 0T: 1 way (HHHH)
0H, 1T: 1 way (TTTT)

There are your 16 ways. 15/16 involve heads. Aren't you glad we have the 1-x trick?

tiamo2015 · Answer

Thank you all for the answer and explanation, but I'm a bit confused as I've looked up few sources on the Internet (not relating to GMAT), and they all indicated the chance of getting 1 head in 4 flips of a coin is 4/16 = 1/4 , I'm quoting here from a site linked to University page:

What is the difference here? is it the "at least" phrase?

DmitryFarberMPrep · Answer

What you're looking at there is the chance of getting heads  exactly  once, as opposed to  at least  once. That chance is represented by the first item in my list:

1H, 3T: 4 ways (heads first, second, third, or fourth)

ScottTargetTestPrep · Answer

We can use the formula:

P(at least one head on 4 flips) = 1 - P(no heads on 4 flips)

P(no heads on 4 flips) = (1/2)^4 = 1/16.

P(at least one head on 4 flips) = 1 - 1/16 = 15/16.

Answer: E

Kinshook · Answer

Given: John flips a coin 4 times.

Asked: What is the probability that he gets heads on at least one of the four flips?

Probability of getting no heads on 4 flips = (1/2)^4 = 1/16

the probability that he gets heads on at least one of the four flips = 1 -1/16 = 15/16

IMO E

Poju4real · Answer

The probability of having heads on at least one of the 4 flips = 1- the probability of having all tails in 4 flips.
 = 1-(1÷16)
 = 15/16.

Posted from my mobile device

CrackverbalGMAT · Answer

The probability of getting a heads at least once = 1 - probability of getting tails the four times
P(Head)= 1/2
P(Tail)=1/2
Getting a tail in 4 counts = 1/2 * 1/2 *1/2 *1/2= 1/16

Thus, the probability of getting a heads at least once = 1-1/16 = 15/16
 (option e)

D.S
GMAT SME

BelalHossain046 · Answer

Event: he gets heads on at least one of the four flips
Complement: he gets NO heads on at any of the four flips : (Get Tails in all cases: TTTT).Probability= 1/2*1/2*1/2*1/2=1/16
So, Probability he gets heads on at least one of the four flips= 1- Probability of he gets NO heads on at any of the four flip=1-1/16=15/16

BrushMyQuant · Answer

Given that John flips a coin 4 times, and we need to find What is the probability that he gets heads on at least one of the four flips?

Coin is tossed 4 times => Total number of cases =  2^4  = 16

Now in all the cases except TTTT we get at least one head=> 16 - 1 = 15 cases

=>  P(Getting at least one Head)  =  \frac{15}{16}

So,  Answer will be E 
Hope it helps!

Watch the following video to learn How to Solve Probability with Coin Toss Problems

https://www.youtube.com/watch?v=LRURv38kZw8

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

John flips a coin 4 times. What is the probability that he gets heads

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

John flips a coin 4 times. What is the probability that he gets heads

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards