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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

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  1. hba
    • 2 years ago
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    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
    • 2 years ago
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    I think its 1/2.

  3. hba
    • 2 years ago
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    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
    • 2 years ago
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    where do you get the 7 from

  5. hba
    • 2 years ago
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    total number of outcomes

  6. rajathsbhat
    • 2 years ago
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    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
    • 2 years ago
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    and how do you get the total number of outcomes

  8. hba
    • 2 years ago
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    |dw:1344087828228:dw|

  9. hba
    • 2 years ago
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    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
    • 2 years ago
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    Oh okay, I understand now. Thank you.

  11. hba
    • 2 years ago
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    You are welcome

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