Each of the problems below is meant to be similar to the problems you
have already seen worked out, either

in earlier homeworks or in lecture. Reveiw those problems to
find the similarities if you are stuck.

1) [15 pts] A student is taking a multiple choice exam.
Each question has 4 possible answers.

Assume that the student has not studied, and is guessing blindly.
If the exam has 10 questions,

a) What is the probability that the student gets all answers correct?

b) What is the probability that the student gets all answers wrong?

c) What is the probability that the student gets more than one answer
wrong?

2) [15 pts] A jar contains 2 red balls, 2 blue balls, and 2 green
balls. A blindfolded person comes and randomly

draws three balls from the jar. The order in which the balls
are drawn does not matter.

a) What is the probability that the three balls are all of different
color?

b) What is the probability that two of the balls are blue and the third
is red?

c) What is the probability that two balls are the same color and the
third is not?

3) [20 pts] You are dealt 5 cards from an ordinary, randomly shuffled, 52 card deck.

a) What is the probability that the first card is a Jack, and the 5th
card is a six, and the other cards are

neither Jacks nor sixes?

b) What is the probability that in the five cards there will be exactly
one Jack and one six?

c) What is the probability that in the five cards there will be exactly
two Jacks and one six?

d) What is the probability that in the five cars there will be no Jacks
or sixes?