Huge probability question! Help!?

μ = np (Average = How many questions there are * the probability)

μ = 15 * (1/5)

μ = 3 answers correct

σ = sqrt((p*(p - 1)) / n) (Standard deviation = Probability * 1 - probability divided by the number of questions, then square root your answer)

σ = sqrt((1/5)(4/5) / 15)

σ = 0.1033

A student guessing each problem would have a 1/5 chance of getting it right. If he guessed a second time, it would become 1/5 * 1/5 = 1/25, just like if you flip a coin twice, you have a 1/4 chance of getting both heads [1/2 *1/2 = 1/4]. the question becomes (1/5)^15, the 1/5 being the chance he gets it right, and 15 being the number of questions right.

1/30517578125 that he'll get it completely right.

a.

The student still has a 20% chance of getting the problem right if he answers the same on all the questions, so the instant probability. So he can expect a 20% of getting it right.

b.

1/5 * 1/5 = 1/25

This is 2 problems with 5 multiple choice answers.

Repeat this 15 times and you'll get the probablity he'll get it all right, but this is also the probability that he'll get it all wrong, then there's everything in between.

a.

15 x (1/4) = 3.75 =4 (round up)

b.

s.d

= npq

= 15(1/4)(3/4)

= 2.8125