If a certain coin is flipped, each of the probabilities that the coin

Question

If a certain coin is flipped, each of the probabilities that the coin will land heads or tails is 1/2. If the coin is flipped 4 times, what is the probability that it will land twice tails up on the 4 flips?

A. 3/8
B. 1/16
C. 1/2
D. 5/8
E. 11/16

A. 3/8 
B. 1/16 
C. 1/2 
D. 5/8 
E. 11/16

msk0657 · Answer

If the coin is flipped 4 times then total probability scenarios will be 2^4 times..

Now probability that it will land twice tails up on the 4 flips = 4!/ 2! * 2! - total cases / tails repetition and heads preposition => 6

Possible cases / Total probability = 6/ 2^4 = 3/8.

Option A.

MathRevolution · Answer

==> Just like HHTT, out of 4 flips, the chances of getting 2 heads and 2 tails is 6 (4!/2!2!=6) in HHTT. If so, the chances of getting HHTT is (1/2)(1/2)(1/2)(1/2)=1/16, and 1/16*6=3/8. Therefore the answer is A. 
 Answer: A

ThatDudeKnows · Answer

4 tails: 1/16
3 tails, 1 head: 4/16
1 tail, 3 heads: 4/16
4 heads: 1/16

Sum: 10/16

What's left? 6/16 = 3/8

Answer choice A

samarth1222 · Answer

Hey,
How did you calculate the probability of 3 tails 1 head and 1 head 3 tails?

naveeng15 · Answer

If the coin is flipped 4 times then total probability scenarios will be 2^4 times..

Now probability that it will land twice tails up on the 4 flips = 4!/ 2! * 2! - total cases / tails repetition and heads preposition => 6

Possible cases / Total probability = 6/ 2^4 = 3/8

ThatDudeKnows · Answer

samarth1222

There are four ways to order four things where three of them are the same and the fourth one is different:
XXXO
XXOX
XOXX
OXXX

gmatpro15 · Answer

since the outcomes can be counted its better to list

or you can use binomial formula 
nCr p^r(1-p)(n-r)

= 4c2 (1/2)^2(1/2)^2 = 6(1/4)(1/4) = 3/8

BrushMyQuant · Answer

If a certain coin is flipped, each of the probabilities that the coin will land heads or tails is 1/2. If the coin is flipped 4 times

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

What is the probability that it will land twice tails up on the 4 flips?

=> We have 4 flips and we need to find two flips out of 4 in which we need to get tails
=> We can do that by choosing 2 places out of 4 in 4C2 ways =  \frac{4!}{2!*2!}  = 2*3 = 6 ways

P(2T in 4 flips) =  \frac{6}{16}  =  \frac{3}{8}

So,  Answer will be A 
Hope it helps!

Playlist on Solved Problems on Probability  here

Watch the following video to MASTER Probability with Coin Toss Problems

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

If a certain coin is flipped, each of the probabilities that the coin

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GMAT Problem Solving (PS) Questions

If a certain coin is flipped, each of the probabilities that the coin

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