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.

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,

$n+3n+8n=240$

$12n=240$

$n=\dfrac{240}{12}$

$n=20$

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:

$P(Red)=\dfrac{20}{240}$

$P(Red)=\dfrac{1}{12}$

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

$E(Red)=1000\times P(Red)$

$E(Red)=1000\times \dfrac{1}{12}$

$E(Red)=83.333...$

$E(Red)\approx 83$

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