Probability

Question

A spinner and a cube are used in a game. If the probability of a player spinning the color red and then rolling a 5 or 6 is 1/8, how many sections of the spinner should be labeled with the color red?

Answer 1

Let n = the number of sectors (congruent pie-shaped parts of the circular face of the spinner).

Let the number of red sectors be r.

Probability of spinning red = r/n.

Prob(5 or 6 rolled on one normal die) = 1/3 (i.e. two out of six)

 

P(red on spinner, 5 or 6 on die) = (r/x)(1/3)

r/(3x) = 1/8

(r/x) = 3/8

 

So one answer is that the spinner ought have three red sectors, out of eight sectors, each having a 45^o central angle.

 

Other answers could exist: 6 red sectors out of sixteen, etc.