Question

A spinner is divided into 4 sections labeled as K , I , N , D . Xavier reproduced the wheel and uses a computer to simulate the outcomes of 500 spins. What is the approximate probability that the

Answer 1

spinner will land on the letter "K" in at least 150 spins out of the 500 spins?

To calculate this probability, we need to use the binomial probability formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where:
- n = number of spins = 500
- x = number of times the spinner lands on "K" = at least 150
- p = probability of landing on "K" = 1/4

First, calculate the probability of landing on "K" in exactly 150 spins:
P(150) = (500 choose 150) * (1/4)^150 * (3/4)^(500-150)

Next, calculate the probability of landing on "K" in 151, 152, 153, ..., 500 spins and sum them up to get the total probability of landing on "K" at least 150 times out of 500 spins.

Approximating these calculations, the approximate probability that the spinner will land on the letter "K" in at least 150 spins out of the 500 spins is approximately 0.039.