Question

A game consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12; as shown below.       

 
If the outcomes are equally likely, find the probability that the pointer will point at:

1. 6
2. an even number.
3. a prime number.
4. a number greater than 8.
5. a number less than or equal to 9.
6. a number between 3 and 11.

Answer 1

Total number of possible outcomes = 12 

i. Number of favorable outcomes for 6 = 1 

P(the pointer will point a 6) = `1/12` 

ii. Favorable outcomes for an even number are 2, 4, 6, 8, 10, 12 

Number of favorable outcomes = 6 

P(the pointer will be at an even number) = `6/12 = 1/2`

iii. Favorable outcomes for a prime number are 2, 3, 5, 7, 11 

Number of favorable outcomes = 5 

P(the pointer will be at a prime number) = `5/12` 

iv. Favourable outcomes for a number greater than 8 are 9, 10, 11, 12 

Number of favorable outcomes = 4 

P(the pointer will be at a number greater than 8) = `4/12 = 1/3`

v. Favorable outcomes for a number less than or equal to 9 are 1, 2, 3, 4, 5, 6, 7, 8, 9 

Number of favorable outcomes = 9

P(the pointer will be at a number less than or equal to 9) = `9/12 = 3/4` 

vi. Favorable outcomes for a number between 3 and 11 are 4, 5, 6, 7, 8, 9, 10 

Number of favorable outcomes = 7 

P(the pointer will be at a number between 3 and 11) = `7/12`