Some probability problems have conditions that must be addressed during solving. The following textbook examples demonstrate this concept.

 

Read pages 154-156 Example 2 and pages 157-158 Example 4 in your textbook, Principles of Mathematics 12 .

Complete the Your Turn questions on page 156 (a & b) and page 158 for more practice solving probability with conditions.

Click here to verify your answers .

 

There is often more than one way to solve a problem. Example 5 explores this.

An MP3 player, a backpack, and a basketball have been donated to a school for door prizes at an upcoming dance. There are 200 people attending the dance, and all place their ticket stubs into the draw box. Assuming the tickets are not replaced after the draw, what is the probability of winning any one of the prizes?  


 

Method 1:

The probability of winning any one of the prizes is the probability of winning the first prize, winning the second prize, or winning the third prize. After each draw, the number of tickets remaining decreases by one. These are dependent events.

P (winning 1 prize) = P (winning 1 st prize) or P (wining 2 nd prize) or P (winning 3 rd prize)

P (winning 1 prize) = P (winning 1 st prize) + P (wining 2 nd prize) + P (winning 3 rd prize)

The probability of winning any one of the three prizes is 0.015.

Method 2:

The number of ways to choose 3 winning tickets is 200 C 3 . There are 199 C 2 ways to choose the other 2 winners and 1 C 1 ways to be one of the winners.

P (winning 1 of the 3 prizes) .

The probability of winning any 1 of the 3 prizes is 0.015.

 

Read pages 152-153 Example 1 in your textbook, Principles of Mathematics 12 .

Complete the Your Turn question on page 154 for more practice solving probability problems using counting techniques.

Click here to verify your answer .

Read pages 203-204 Frequently Asked Questions in your textbook, Principles of Mathematics 12 .