Sam plays a game in which he selects three different numbers from 1 to n (n>3).

 

MCR3U  Sam plays a game in which he selects three different numbers from 1 to n (n>3).

Probability of winning

Instructions:

1. This project is an individual project. Therefore, the students are required to complete this project individually. Evaluation would be performed via the entire procedure.
2. Students are allowed to use calculator only to solve the question effectively.
3. Each student is required to hand in ananswer sheet for all the questions. The sheet should include the process of demonstration and question solving procedure.
4. This task is 100 marks in total.

 

Sam plays a game in which he selects three different numbers from 1 to n (n>3). After he selects his numbers, four different winning numbers from 1 to n are chosen, one at a time. Sam wins if all three of his numbers are among the winning numbers. His probability is now given by

P(n) = ÷ –

Question:

Calculate the amount of work done in each situation.

 

3. Simplify polynomial expression P(n). (A3.1)(k)(25 p)
4. Verify the numerator of the first part of the expression is equal to 1.633. You should verify this by a demonstration process and by calculator. (A3.2)(k,t)(25 p)
5. After simplify rational expression, state the restrictions on n. (A3.3)(k,t)(25 p)
6. Determine if the expression -is equivalent to P(n). (A3.4)(k,t)(25 p)