Question

Emilia is designing a prize wheel for her school. 200 students will spin the wheel once each. Emilia wants the expected number of winners to be 90. If the wheel is split into 40 equal-sized sections, how many of the sections should be marked as "win"?​

Answer 1

If Emilia wants the expected number of winners to be 90 out of 200 students, then the probability of winning must be 90/200 = 0.45.

Since the prize wheel is split into 40 equal-sized sections, the probability of winning on any given spin is 1/40 = 0.025.

Therefore, we can set up the equation:

0.025x = 0.45

where x is the number of sections marked as "win".

Solving for x, we get:

x = 0.45/0.025 = 18

So, Emilia should mark 18 of the 40 sections as "win" in order to achieve an expected number of 90 winners out of 200 spins.