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March 26, 2017

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When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below:

HHHH HHHT HHTH HHTT
HTHH HTHT HTTH HTTT
THHH THHT THTH THTT
TTHH TTHT TTTH TTTT



Let X denote the total number of tails obtained in the four tosses. Find the probability distribution of the random variable X. Leave your probabilities in fraction form.

  • math - ,

    As you mentioned, there are 16 possible outcomes each with equal probability.

    For X=0, there is only one case out of sixteen, namely HHHH. Therefore
    X(0)=1/16.

    For X=1, you will count the number of cases where T occurs only once. You should count 4 of such cases, therefore
    X(1)=4/16=1/4

    Repeat the calculation for X=2,3,4 and obtain the values of X(2), X(3), and X(4).

    The sum of the values X(0) to X(5) should equal to 1.

  • math - ,

    If there are 16 possible outcomes for the 4 tosses, the probability of getting 4 tails = 1/16, 3 tails = 4/16 = 1/4, 2 tails = ?, 1 tail = ?, no tails = ?.

    I'll let you calculate the remaining fractions.

    As a check, the sum of these fractions must = 1.

    I hope this helps.

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