On one side of a coin there is the number 0 and on the other side the

Question

On one side of a coin there is the number 0 and on the other side the number 1. What is the probability that the sum of three coin tosses will be 2?

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

BrentGMATPrepNow · Accepted Answer

Let's examine ONE CASE in which we get a sum of 2. 
How about getting 0 then 1 then 1
Now let's determine the probability of this one case.

P(getting 0 then 1 then 1) = P(1st toss is 0   AND   2nd toss is 1   AND   3rd toss is 1) 
= P(1st toss is 0)   AND   P(2nd toss is 1)   AND   P(3rd toss is 1) 
 = 1/2   x   1/2   x    1/2
=  1/8 
Of course, we've only examined ONE CASE so far.

Now consider the fact, that we can arrange one 0 and two 1's in 3 different ways: {0, 1, 1}, {1, 0, 1} and {1, 1, 0}
Each of these  3  possibilities is equally likely.

So, P(sum is 2) = ( 1/8 )( 3 )
= 3/8
Answer:  D

14101992 · Answer

Assume the coin is unbiased.

Possible sums from 3 tosses = 0,1,2,3

O and 3 are possible in only 1 case each. (0,0,0 or 1,1,1)
1 is possible in 3C1 = 3 cases. (1,0,0; 0,1,0 or 0,0,1) or 
similarly, 2 is possible in 3C2=3 cases (1,0,1; 1,1,0; 0,1,1)

So answer will be 3/8. Option D.

CounterSniper · Answer

P(getting a zero) = p(0)=1/2*1/2*1/2=1/8 (one possible way)
p(getting a sum of 3) = p(3) = 1/2*1/2*1/2=1/8 (one possible way)
p(getting a sum of 1) = p(1) = 3*(1/2*1/2*1/2) (3 possible ways)
p(getting a sum of 2) = 1-{p(0)+p(3)+p(1)} 
= 1-5/8 
=3/8

LXVE · Answer

To get a sum of 2 you must flip 1, 1, and 0, but the order in which you flip these numbers does not matter.

Think of this as heads or tails- what is the probability of exactly 2 heads and 1 tails? Well that's P(HHT) which is (1/2)^3 * 3!/2!

Answer is 3/8

Sent from my SM-G928T using  GMAT Club Forum mobile app

b0108 · Answer

This question can be solved more easily without much effort by using a Probability Tree as well to ensure that no combination of coin tosses is missed out.

santro789 · Answer

Can someone explain this with any other method?

Bunuel · Answer

Each of the three tosses can give two results: 0 or 1. So, the total number of outcomes is 2*2*2 = 8.

First toss - Second toss - Third toss
0 - 0 - 0 
1 - 0 - 0
0 - 1 - 0
0 - 0 - 1
 1 - 1 - 0
1 - 0 - 1
0 - 1 - 1 
1 - 1 - 1

As you can see, for the sum of three coin tosses to be 2, two tosses should give 1 and one toss should give 0.

(1, 1, 0) can occur in 3!/2! = 3 ways, which is the number of arrangements of three items out of which two are identical: 
First toss - Second toss - Third toss
 1 - 1 - 0
1 - 0 - 1
0 - 1 - 1 .

The probability = (the number of favourable outcomes)/(the total number of outcomes) =3/8.

Answer: D.

Hope it's clear.

santro789 · Answer

Many Thanks Bunuel for the wonderful explanation.

PAVITHRAN · Answer

If it requires to have the sum of 2
Then arrangement will be (1 1 0)
 {(1/2)(1/2)(1/2)}(3!/2!)
 =(1/8)*3

JeffTargetTestPrep · Answer

The total number of outcomes when flipping three coins is 2 x 2 x 2 = 8. The outcomes yielding a sum of two are (1,1,0), (0,1,1), and (1,0,1). Thus, the probability of a sum of 2 is 3/8.

Answer: D

SchruteDwight · Answer

(0,1,1) can be arranged in 3!/2!=3 ways. 
the total ways are 2^3
Hence, 3/8

BrushMyQuant · Answer

Given that On one side of a coin there is the number 0 and on the other side the number 1. We need to find What is the probability that the sum of three coin tosses will be 2?

As the coin is tossed 3 times => Number of cases =  2^3  = 8 cases

Sum of the three tosses is 2. So following are the possible outcomes
(0, 1, 1), (1, 0, 1), (1, 1, 0)
=> 3 cases

=>  Probability that the sum of three coin tosses will be 2  =  \frac{3}{8}

So,  Answer will be D 
Hope it helps!

The Concept is similar to that of Rolling a dice. Watch the following video to learn How to Solve Dice Rolling Probability Problems

https://www.youtube.com/watch?v=5PVZYQXet18

bumpbot · Answer

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