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) ½.
c) 1/5.
d) 3/8.
e) 1/3.
I got this problem from a document and don't remember the source. So, I am not 100% sure about the options and the provided answer.
But before looking at the options, I came up with the answer of 1/4. My logic is that we can have only 4 different total: 0,1,2 and 3 from three flips. So the probability of getting a total of 2 is 1/4. Could you please point out where I am making the mistake? I feel that my approach is faulty, but can't figure it out properly. Please help me.
The answer given for this problem is [spoiler](d)[/spoiler].
Probability: Total of 3 coin flips
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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?
No of ways sum of three coin tosses will be 2 are 3
011
101
110
Probable totals of three coin tosses will be 8
000
111
010
001
100
110
101
011
Probability = 3/8
No of ways sum of three coin tosses will be 2 are 3
011
101
110
Probable totals of three coin tosses will be 8
000
111
010
001
100
110
101
011
Probability = 3/8