Question

3 fair coins are tossed. What's the probability of obtaining at most 2 heads?

Answer 1

1/8

Answer 2

how did you get that?

Answer 3

There are 8 possible ways to toss 3 coins and they are


HHH
HHT
HTH
HTT


THH
THT
TTH
TTT


Of this list, there are 7 ways to get either 1 head or 2 heads


So the probability is 7/8

Answer 4

because when you are doing probability, you need to multiply the chance that it will be heads, which is 1 out of 2 or 1/2. therefore it is 1/2 *1/2 which is 1/4 times 1/2 which is 1/8. this is the probability that all of the answers are heads

Answer 5

Alternatively, you can compute the probability of getting all tails, which is (1/2)*(1/2)*(1/2) = 1/8


Then subtracting that from 1 to get 1 - 1/8 = 7/8


getting the same answer

Answer 6

but isn't that just exactly 2 heads and not at most 2 heads?

Answer 7

oh wait, the probability is still the same, I just mixed up HHH and TTT

Answer 8

@Jim In the list of possibilities, you have HHH counted as one of the "either 1 or 2". Does that mean that the probability is 6/8?

Answer 9

I mixed up HHH and TTT on accident


I meant to write...


There are 8 possible ways to toss 3 coins and they are


HHH
HHT
HTH
HTT

THH
THT
TTH
TTT


Of this list, there are 7 ways to get 0 heads, 1 head or 2 heads (ie "at most 2 heads")


Basically, it's everything but HHH.


So the probability is 7/8

Answer 10

So you can see that the probability is still the same.

Answer 11

oh. TTT is still at most 2 heads. Thank you.

Answer 12

Yes as 0 heads is less than that upper max limit.

Answer 13

my bad! i thought that it said all heads! my bad! therefore , the probability is 7/8