Question

A multiple choice test has 65 questions and each question has 6 possible answer choices, only 1 of

which is correct. If a student guesses on every question, how many questions should he expect to get

wrong?

A baseball player has a 0.25 batting average. If he is at bat 4 times, then:

a) What is the probability that the player will have at least 2 hits?

b) What is the probability of at least 1 hit?

c)What is the expected number of hits at bat?

Answer 1

#1.
probability of guessing wrong answer = 5/6

expected wrong answers = np = 65*5/6
= 54.17

rounding to nearest integer it is 54

#2.
a)
Here, n = 4, p = 0.25, (1 - p) = 0.75 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 2).
P(X >= 2) = (4C2 * 0.25^2 * 0.75^2) + (4C3 * 0.25^3 * 0.75^1) + (4C4 * 0.25^4 * 0.75^0)
P(X >= 2) = 0.2109 + 0.0469 + 0.0039
P(X >= 2) = 0.2617

b)
We need to calculate P(X = 0)
P(X = 0) = 4C0 * 0.25^0 * 0.75^4
P(X = 0) = 0.3164
P(X >= 1) = 1 - 0.3164 = 0.6836

c)
expected number = np = 4*0.25 = 1