Question

A spinner is divided into six equally sized regions. Three of the regions are labeled 4, one region is labeled 3, one region is labeled 1, and the last region is labeled 5. The spinner is spun 720 times. How many times is the spinner expected to land on 4? how many times is the spinner expected to land on a prime number?

SHOW ALL WORK PLEASE!!!!!!!!!!!!!!

Answer 1

Explanation:

To find the expected number of times the spinner is expected to land on a specific outcome, we need to calculate the probability of that outcome and multiply it by the total number of spins.

Given information about the spinner:

Total number of spins: 720

Number of regions labeled 4: 3

Number of regions labeled prime numbers (3 and 5): 2

Expected number of times the spinner lands on 4:

The probability of landing on 4 is the number of regions labeled 4 divided by the total number of regions:

Probability of landing on 4 = 3/6 = 1/2

To find the expected number of times the spinner lands on 4, we multiply the probability by the total number of spins:

Expected number of times landing on 4 = (1/2) * 720 = 360

Therefore, the spinner is expected to land on 4, approximately 360 times.

Expected number of times the spinner lands on a prime number:

The probability of landing on a prime number (3 or 5) is the number of regions labeled prime numbers divided by the total number of regions:

Probability of landing on a prime number = 2/6 = 1/3

To find the expected number of times the spinner lands on a prime number, we multiply the probability by the total number of spins:

Expected number of times landing on a prime number = (1/3) * 720 = 240

Therefore, the spinner is expected to land on a prime number, approximately 240 times.