Posted by Elizabeth on Saturday, December 5, 2009 at 4:29pm.
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.
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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