math
posted by Elizabeth on .
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.

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.