## LMarieee 2 years ago You toss 3 coins . What is the probability that you get exactly 2 heads, given that you got at least 1 head? A tree diagram will help you answer this question

1. hba

There is one possibility where you get no heads. There are three possibilities where you get 1 head. There are three possibilities where you get 2 heads. There is one possibility where you get 3 heads. But we don't count the possibility where you get no heads at all. So we only have seven possibilities that we're dealing with. So, the odds are 3/7.

2. rajathsbhat

I think its 1/2.

3. hba

The tree diagram shows 8 equally likely possible outcomes. We must exclude the TTT outcome because it is given that you get at least 1 head. Count all of the branch paths that show exactly 2 heads. There are 3 of them. There are 7 possible outcomes because we eliminated one of them. Therefore, the probability of getting exactly 2 heads in this problem is 3/7.

4. LMarieee

where do you get the 7 from

5. hba

total number of outcomes

6. rajathsbhat

since you have 1 head, the possibilities withe the other 2 are: HH, HT, TH, TT. Since you need exactly 2 heads, 2 of the above 4 possibilities are desirable. therefore $P=\frac{2}{4}=\frac{1}{2}$

7. LMarieee

and how do you get the total number of outcomes

8. hba

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9. hba

But we don't count the possibility where you get no heads at all. So we only have seven possibilities that we're dealing with.

10. LMarieee

Oh okay, I understand now. Thank you.

11. hba

You are welcome