Deck 7: Discrete Probability

Question 1

A fair red die and a fair blue die are rolled. What is the expected value of the sum of the number on the red die plus three times the number on the blue die?

Answer 1

Question 2

What is the probability that a fair coin lands heads four times out of five flips?

Answer 2

There are 25 possible outcomes of five flips. The number of possible ways to have the coin come up heads four times is the number of ways to pick four flips out of five. This can be done in C(5, 4) = 5 ways. Hence the probability that the coin lands heads four times out of five flips is 5/25 = 5/32.

Question 3

Two identical urns contain balls. One of the urns has 6 red balls and 3 blue balls. The other urn has 5

Answer 3

Question 4

What is the probability that in a group of 200 random people, at least two of them have the same triple of initials (such as RSZ for Ruth Suzanne Zeitman), assuming that each triple of initials is equally likely. Give the answer as a calculation; it is not necessary to evaluate the expression.

Question 5

Suppose that a bag contains six slips of paper: one with the number 1 written on it, two with the number 2, and three with the number 3. What is the expected value and variance of the number drawn if one slip is selected at random from the bag?

Question 6

What is the probability that a random person who tests positive for a certain blood disease actually has the disease, if we know that 1% of the population has the disease, that 95% of those who have the disease test positive for it, and 2% of those who do not have the disease test positive for it.

Question 7

What is the probability that a positive integer less than 100 picked at random has all distinct digits?

Question 8

Two identical urns contain balls. One of the urns has 6 red balls and 3 blue balls. The other urn has 5 red

Question 9

Suppose that two cards are drawn without replacement from a well-shuffled deck. What is the probability that both cards have numbers and that the numbers on the cards are the same (note that only the numbers 2 through 10 are shown on cards, since aces, kings, queens, and jacks are represented by letters).