Chapter 9 Section 3: Applications of Counting

Remember: 1. E represents an event and S represents the sample space for a certain “experiment”.

2. P(E) = n(E) / n(S)

3. The Multiplication Principle states if a task can be broken down into different parts (m1, m2, m3, …, mn),

then the total number of ways to complete the task is m1 x m2 x m3 x … x mn .

We can use the above to help solve applied problems in probability.

1. A club consists of 7 members (4 men and 3 women). A committee of 2 members is chosen at random. Find:

a. P(both members chosen are men) = b. P(both members chosen are women) =

c. P(committee has 1 man and 1 woman) = d. Probability Distribution for and Expected

Numberof men on the committee.

e. P(Bill is on the committee) = e. P(Bill and Tina are on the committee) =

2. In a lottery, 4 numbers are chosen from the numbers 1 – 30. If your ticket matches: 2 numbers you win $10, 3 numbers

you win $50, all 4 numbers you win $1,000. You win $0 otherwise. Construct the Probability Distribution for the lottery and

find the Expected Winnings for a ticket.

3. DVDs use microchips. A DVD manufacturer rejscts a package of 24 microchips is in a sample of 8, at least 1 is defective.

If a package of 24 microchips has 3 defective chips, find the probability the package is accepted (not rejected).

P(accept package) =

4. What should the DVD manufacturer do to decrease the risk of accepting a package with defective chips?