Question

Assume that there are 7 different issues of Sports Illustrated magazine, 8 different issues of Newsweek, and 4 different issues of Time, including the December 1st issue, on a rack. You choose 4 of them at random. (1) What is the probability that exactly 1 is an issue issue of Sports Illustrated?

Answer 1

The probability is 0.3973

Explanation:

We are going to solve this using counting theory.

If A is an event ⇒
`P(A)=(CasesWhenAOccurs)/(TotalCases)`

If an experiment 1 can takes place in n1 forms, a second experiment 2 can takes place in n2 forms, ..., a experiment-i can takes place in ni forms :

The total forms to take place all the experiments are n1 x n2 x ... x ni

This is call the multiplication principle

Let's define the combinatorial number :

`nCr = (n!)/(r!(n-r)!)`

nCr number is the way to choose r objects from a set of n objects

Now let's define the event A : ''1 is an issue of Sports Illustrated when I choose 4 of them at random''

From 7 different issues of Sports Illustrated I choose 1

From the others issues (8+4) I choose 3

`P(A) = (7C1.12C3)/(19C4)`

19C4 number is the way to choose 4 issues from a set of 19

The probability exactly that 1 is an issue of Sports Illustrated is

`P(A)=(7C1.12C3)/(19C4) =0.3973`