Question

Kevin has a spinner that has 10 equal sections and 2 sections of each color—red, blue, green, yellow, and purple. Kevin spins the spinner 180 times. Kevin determines about how many times the spinner will land on red or green, and his work is shown below.

Answer 1

Kevin's spinner will land on red or green approximately 72 times out of 180 spins since the probability of landing on red or green per spin is 0.4.

Step-by-step explanation:

The student's question involves determining the expected number of times a spinner will land on specific colors, given that the spinner is spun a large number of times. In this scenario, Kevin has a spinner with 10 equal sections with 2 sections of each color - red, blue, green, yellow, and purple. When Kevin spins the spinner 180 times, he wants to figure out how many times it will land on red or green.

Since there are 2 sections each of red and green out of a total of 10, the probability of landing on either red or green for a single spin is P(red or green) = P(red) + P(green) = 2/10 + 2/10 = 4/10 = 0.4. To find the expected number of times the spinner will land on red or green after 180 spins, we simply multiply the total number of spins by the probability of landing on red or green: 180 spins * 0.4 = 72 spins. Therefore, we can expect the spinner to land on red or green approximately 72 times out of 180 spins.

Answer 2

From the problem, the way the spinner is set up could be

red red blue blue green green yellow yellow purple purple

with two sections of each color and 10 total equal sections.

From this we know that 4 out of the 10 sections are red or green.
That means that there is a 4/10 chance of getting a green or a red every time Kevin spins.

Multiply 180 by 4/10 and you get 72.

The spinner will land on red or green about 72 times.

Hope this helps!