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    sirinivas's Avatar
    sirinivas Posts: 21, Reputation: 1
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    #1

    Aug 22, 2010, 11:02 PM
    if 10 coins are tossed what is the probability of getting 7 heads
    if 10 coins are tossed what is the probability of getting 7 heads?
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #2

    Aug 23, 2010, 04:22 AM

    For this, you have to use the binomial distribution.

    Let X be the event that a head is obtained.

    X ~ B (10, 0.5)

    10 because there are 10 tosses and 0.5 because the probability of getting a head in each toss is 0.5.

    The, find P(X = 6).

    Can you work this out?

    EDIT: I made a typo. This should read as:
    Then, find P(X = 7).
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #3

    Aug 23, 2010, 02:16 PM

    You can think this problem through as follows:

    You toss a coin 10 times and want to get exactly 7 heads and 7 tails. The probability of getting either with each flip is 0.5. So to get 7 heads and then 7 tails in that order is:



    But in this problem we don't care about order. So multiply this by the number of ways that you can arrange the 7 heads and 3 tails in 10 coin flips - that number is C(10,3), or:


    So the probability of getting 7 heads and 3 tails in any order is:


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