Question

A spinner has 10 equally sized sections, 5 of which are gray and 5 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue? Write your answer as a fraction in the simplest form.

Answer 1

`P(Gray\ and\ Blue) = (1)/(4)`

Explanation:

Given

`Sections = 10`

`n(Gray) = 5`

`n(Blue) = 5`

Required

Determine P(Gray and Blue)

Using probability formula;

`P(Gray\ and\ Blue) = P(Gray) * P(Blue)`

Calculating P(Gray)

`P(Gray) = (n(Gray))/(Sections)`

`P(Gray) = (5)/(10)`

`P(Gray) = (1)/(2)`

Calculating P(Gray)

`P(Blue) = (n(Blue))/(Sections)`

`P(Blue) = (5)/(10)`

`P(Blue) = (1)/(2)`

Substitute these values on the given formula

`P(Gray\ and\ Blue) = P(Gray) * P(Blue)`

`P(Gray\ and\ Blue) = (1)/(2) * (1)/(2)`

`P(Gray\ and\ Blue) = (1)/(4)`