Question

PLEASE HELP ME WITH THIS MATH PROBLEM!!!!

Marcus plays a game in which he spins a spinner over and over again. The spinner has 4 equally sized sections labeled E, F, G, and H. Spinning an E six times means the game is over.

Marcus uses a uniform probability model to predict the number of times the spinner will be spun before the letter E appears 6 times.

What is Marcus's prediction for the number of total spins before the letter E appears 6 times?

10 spins

18 spins

24 spins

30 spins

Answer 1

Answer- 24 spins

The probability of getting an E on a single spin is 1/4. The probability of not getting an E on a single spin is 3/4.

To find the expected number of spins before getting 6 E's, we can use the negative binomial distribution.

The formula for the expected value of a negative binomial distribution is:

E(X) = r * (1/p)

where:

- X is the random variable representing the number of spins until the 6th E appears

- r is the number of successes we want (in this case, 6)

- p is the probability of success (in this case, 1/4)

E(X) = 6 * (1/(1/4)) = 24

Therefore, Marcus's prediction for the number of total spins before the letter E appears 6 times is 24.

So the answer is 24 spins.