John tossed a fair coin 3 times. What is the probability that the outc

Question

John tossed a fair coin 3 times. What is the probability that the outcome was “tails” exactly twice?

A. 1/8
B. 1/4
C. 3/8
D. 1/2
E. 9/10

siddharthharsh · Answer

Total number of outcomes = 2*2*2 = 8
Number of favorable outcomes = Number of ways two places (for tails) can be chosen out of 3 slots = 3C2 = 3
So probability = 3/8

Alternative 
Probability of getting tail in single toss = 1/2
Probability of getting head in single toss = 1/2

Probability of getting First Tail = 1/2
Probability of getting Second tail (Such that first tail has occurred, this incidentally is also the probability when first was head and second is tail) = 1/2 * 1/2 = 1/4
Probability of getting Third Head ( such that first was tail and second was tail) = 1/2 * 1/2 * 12 = 1/8

As you can notice the probability will be 1/8 whatever the sequence of Heads and tails.
We can arrange 2 Tails and one head in 3 ways (3C2 ways OR (3P3)/2! OR enumeration, whichever method you prefer to get here)

Since the favorable even can happen in either of these 3 ways, so Probability = 3 * 1/8 = 3/8

Shrivathsan · Answer

Total outcomes : 2^3 = 8

HHH 
HHT
HTH
THH
TTH
THT
HTT
TTT

Exactly 2 tails are 3/8

testprepabc · Answer

There are three possible scenarios here: 1) "Tails" on toss 1 and 2, and "Heads" on toss 3: OR (1/2)*(1/2)*(1/2)=1/8 2) "Tails" on toss 1 and 3, and "Heads" on toss 2: OR (1/2)*(1/2)*(1/2)=1/8 3) "Tails" on toss 3 and 2, and "Heads" on toss 1: OR (1/2)*(1/2)*(1/2)=1/8 That's a total probability of (1/8)+(1/8)+(1/8)=3/8 Alternately, you can count: Only possible situation are: HTT, THT, TTH of the possible 8 outcomes. Hence 3/8. Hope it helps

ScottTargetTestPrep · Answer

We need to determine the following:

P(TTH) = (1/2)^3 = 1/8

Since TTH can be arranged in 3!/2! = 3 ways, the probability is 3 x (1/8) = 3/8.

Answer: C

BrushMyQuant · Answer

Given that John tossed a fair coin 3 times and we need to find What is the probability that the outcome was “tails” exactly twice? 
 
Coin is tossed 3 times => Total number of cases =  2^3  = 8

To find the cases in which the coin lands on tails exactly twice we need to select two places out of three _ _ _ in which we will get tails.

This can be done in 3C2 ways =  \frac{3!}{2!*(3-2)!}  =  \frac{3*2!}{2!*1!}  = 3 ways

=> P(2T) =  \frac{3}{8}

So,  Answer will be C 
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 tossed a fair coin 3 times. What is the probability that the outc

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 tossed a fair coin 3 times. What is the probability that the outc

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