Answer to Question #168836 in Statistics and Probability for Rustom

Question

Four coins are tossed. Let A be the random variable representing the

number of heads that occur. Find the values of the random variable A. PossibleOutcomes

Value of the Random Variable A

(Number of Heads)

Answer 1

Four coins are tossed. For each toss, the outcome belongs to one of the following:

{Head, Tail}

We want to count the total number of heads obtained from those 4 tosses. A is the random variable representing the number of heads that occur. We want to find all possible values of A.

Observe that any one of the following cases may happen:

• All the four outcomes are 'Tail'. So the number of heads is 0. Hence, A=0 in this case.
• Any 3 of the 4 outcomes are 'Tail' and the remaining one is a 'Head' Hence, A=1 in this case.
• Any 2 of the 4 outcomes are 'Tail' and the remaining two are 'Head' Hence, A=2 in this case.
• Any 1 of the 4 outcomes is 'Tail' and the remaining three are 'Head' Hence, A=3 in this case.
• All the four outcomes are 'Head'. So the number of heads is 4. Hence, A=4 in this case.

Note that, the 5 cases listed above explores all possible outcomes. Hence, the random variable A takes any one value from{0,1,2,3,4}.