Question

In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at 

i. 8. 

ii. an odd number. 

iii. a number greater than 2. 

iv. a number less than 9.

     

Answer 1

Sample space (S) = {1,2, 3, 4, 5, 6, 7, 8} 

∴ n(S) = 8 

i. Let A be the event that the spinning arrow comes to rest at 8.

∴ A = {8}

∴ n(A) = 1

∴ P(A) = \(\frac{n(A)}{n(S)}\)

∴ P(A) = 1/8

ii. Let B be the event that the spinning arrow comes to rest at an odd number.

∴ B = {1,3,5,7}

∴ n(B) = 4

∴ P(B) = \(\frac{n(B)}{n(S)}\) = 4/8

∴ P(B) = 1/2

iii. Let C be the event that the spinning arrow comes to rest at a number greater than 2.

∴ C = {3,4,5,6,7,8}

∴ n(C) = 6

∴ P(C) = \(\frac{n(C)}{n(S)}\) = 6/8

∴ P(C) = 3/4

iv.  Let D be the event that the spinning arrow comes to rest at a number less than 9. 

∴ D = {1,2, 3, 4, 5, 6, 7, 8}

∴ n(D) = 8 

∴ P(D) = \(\frac{n(D)}{n(S)}\) = 8/8

∴ P(D) = 1

∴P(A) = 1/8; P(B) = 1/2; P(C) = 3/4; P(D) = 1