Question

A biased 3-coloured spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times.

If you spin this spinner 1000 times, how many times do you expect it to land on Red?
(Hint: Find n first)

Answer 1

Given:

A biased 3-colored spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times.

To find:

The expected number of times it land on Red if you spin this spinner 1000 times.

Solution:

A biased 3-colored spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times. So,

`n+3n+8n=240`

`12n=240`

`n=(240)/(12)`

`n=20`

The value of n is 20. It means the spinner land on red 20 times if the spinner was spun 240 times. So, the probability of getting red is:

`P(Red)=(20)/(240)`

`P(Red)=(1)/(12)`

If you spin this spinner 1000 times, then the expected number of times to getting red is:

`E(Red)=1000* P(Red)`

`E(Red)=1000* (1)/(12)`

`E(Red)=83.333...`

`E(Red)\approx 83`

Therefore, the expected number of times to land on red is 83.