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 e…

Question

asked Sep 28, 2022 73.1k views

1 Answer

Ali Lotfi · Answer 1 · 2022-10-03T01:59:34+0000

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.