(Question from Mathematics for the international student Mathematics SL. Third Edition)
Consider tossing three coins simultaneously. The random variable under consideration is the number of heads that could result.
a) List the possible values of X.
This question may seem a bit confusing because they don’t define what X is. From the context, we can assume that X is the random variable, ie: the number of heads that could result. Therefore, X=0,1,2,3 (a head can be tossed 0, 1, 2 or 3 times)
b) Tabulate the possible outcomes and the corresponding values of X.
| X=0 | X=1 | X=2 | X=3 |
|---|---|---|---|
| TTT | TTH | THH | HHH |
| THT | HTH | ||
| HTT | HHT |
c) Find the values of P(X=x), the probability of each x value occurring.
From the above table, we can see that there are 8 total outcomes. Counting the number of outcomes in each column:
P(X=0) = 1/8
P(X=1) = 3/8
P(X=2) = 3/8
P(X=3) = 1/8
d) Graph the probability distribution P(X=x) against x as a probability column graph.
