# math

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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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