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.