Question

You toss 3 coins. What is the probability that you get exactly 2 heads, given that you get at least 1 tail. Use a tree diagram and write as a reduced fraction.

Answer 1

when I list all of the possible outcomes, there are only 8
hhh
hht
hth
htt
thh
tht
tth
ttt
of these 8 there, there are 2 that possibly fit the criteria, but I am confused if only the first coin has to be listed as t, if so, wouldn't it be 1/8?

Answer 2

Your sample space is correct.

Answer 3

i can't figure out the tree diagram part, but I understand the listing! Is 1/8 correct?

Answer 4

But you can have at least one T on any of the three, so THH or HTH or HHT. Note that at least one T in this case means exactly one T. 1/8 is not correct.

Answer 5

P(THH)+P(HTH)+P(HHT)=3/8

Answer 6

I see! That seems so much easier than the tree diagram. Thanks!

Answer 7

there are 7 that have at least 1 tail; so this becomes our sample space. 3 of those have exactly 2 heads; so id say 3/7

Answer 8

3/8
--- = 3/7
7/8