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

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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.
[Reveal] Spoiler: OA

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Re: On one side of a coin there is the number 0 and on the other side the [#permalink]

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New post 12 Jul 2016, 03:46
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.
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Re: On one side of a coin there is the number 0 and on the other side the [#permalink]

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New post 13 Jul 2016, 07:29
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
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Re: On one side of a coin there is the number 0 and on the other side the [#permalink]

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Bunuel wrote:
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.


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:
[Reveal] Spoiler:
D


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Re: On one side of a coin there is the number 0 and on the other side the [#permalink]

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New post 13 Jul 2016, 17:36
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

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Re: On one side of a coin there is the number 0 and on the other side the [#permalink]

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New post 27 Aug 2017, 04:14
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.
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Re: On one side of a coin there is the number 0 and on the other side the [#permalink]

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New post 28 Sep 2017, 03:19
Can someone explain this with any other method?
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Re: On one side of a coin there is the number 0 and on the other side the [#permalink]

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santro789 wrote:
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.

Can someone explain this with any other method?


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.
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: On one side of a coin there is the number 0 and on the other side the [#permalink]

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New post 28 Sep 2017, 03:42
Many Thanks Bunuel for the wonderful explanation.
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Re: On one side of a coin there is the number 0 and on the other side the [#permalink]

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New post 29 Sep 2017, 23:41
santro789 wrote:
Can someone explain this with any other method?


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
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Re: On one side of a coin there is the number 0 and on the other side the [#permalink]

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New post 03 Oct 2017, 08:29
Bunuel wrote:
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.


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
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Re: On one side of a coin there is the number 0 and on the other side the   [#permalink] 03 Oct 2017, 08:29
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