SOLUTION: A fair coin is tossed 3 times in a row. What is the probability that heads appears exactly 2 times? 1/8 3/8 3/16 3/4

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Question 889958: A fair coin is tossed 3 times in a row. What is the probability that heads appears exactly 2 times?
1/8
3/8
3/16
3/4
Found 3 solutions by harpazo, math_tutor2020, greenestamps:
Answer by harpazo(655) About Me  (Show Source):
You can put this solution on YOUR website!
1/2 times 1/2 times 1/2 = 1/8

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

The other tutor is incorrect. The answer is not 1/8.

It is instead 3/8

This is because we have this event space
HHT
HTH
THH
each represents getting exactly two heads.

There are 3 such items in that event space out of 8 total items in the sample space.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are 2 possible outcomes on each toss, so the number of sequences of outcomes on three tosses is 2*2*2 = 8.

Of those 8 possible sequences, 3 of them have exactly 2 heads: HHT, HTH and THH.

So the probability of getting 2 heads on three tosses is 3/8.

Note for this simple example it is easy to see that there are three ways of getting 2 heads, by seeing that the one tail can come up on any one of the three tosses.