Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

Simulate the supply for 20 days using the random numbers below in order to calculate the expected average from 6,68,59,75,96,68,71,71,69,31,28,99,76,38,53,10,78,38,84,65