Practice Problems - Probability

Probabilities with Venn Diagram - from 3.1

For two events A and B we have Pr(A’) = 0.71, Pr(B) = 0.43, and Pr(A U B) = 0.64. Find Pr(A ∩ B).

Probabilities with Venn Diagram - Elite Club - from 3.1

An applicant for Steve’s elite private club may be rejected because he/she is too tall, too short, or too stupid. 60% of the applicants are rejected. Of all applicants, 15% are too tall, 20% are too short, and 40% are too stupid. How many percent of them are rejected because of failing a height requirement and the intelligence requirement?

Probabilities and Independence - from 3.2

Two independent events A and B have probabilities Pr(A) = 0.3 and Pr(B) = 0.7. Find Pr(A U B).

Probabilities with Venn Diagram and Independence - from 3.2

Suppose A and B are independent events with Pr(A ∩ B) = 0.2, Pr(B) = 0.4. Find Pr(A ∩ B’).

Probabilities with Venn Diagram and Independence - Unusual Dresses - from 3.2

On any given day, Mark wears a dress to class with a probability 0.6, and Peter wears earrings to class with a probability 0.5 (Don’t ask lol). They make their decision about those “unusual” dress code independently. What’s the probability that Mark wore dress to class and Peter didn’t wear earrings?

Advanced Probabilities and Independence - from 3.2

Pr(A) = 0.5, Pr(A U B) = 0.65. It is known that A and B are independent. What is Pr(B)?

Probabilities with Tree Diagram - from 3.3

A fair coin is flipped until there are two consecutive tails or a total of four flips, and the result of each flip is noted. The event E consists of those outcomes with exactly 2 tails. Find Pr(E).

Probabilities with Tree Diagram - from 3.3

Three men toss a fair coin to see who pays for lunch. If all three match, they toss again. Otherwise, the "odd man" pays for lunch. What is the probability that they will need to do this more than once? and what is the probability of tossing at most twice?

Slots/Multiplication Principle - from 3.3

Mark, Nicole, Patrick, Rita, Sarah, Ulrich, and Vera are going to attend a conference at a Hilton Hotel. Each one will have a single room by herself or himself. When they arrive at the hotel (they drove together in a company van), there are 6 single rooms available on the sixth floor and 5 single rooms available on the seventh floor. Each person is assigned to one of these rooms.
In how many overall outcomes is Vera on the sixth floor (i.e., Vera's room is on the sixth floor)?
In how many overall outcomes are Patrick and Rita on the same floor?
In how many overall outcomes is Mark on a higher floor than Sarah?

Conditional Probabilities - Spare Tires - from 3.4

The Justin motor company produces 40% of its cars at plant A and the remainder at plant B. Of all cars produced at plant A, 20% do not have a spare tire, while 30% of the cars produced at B do not have a spare tire. A Justin car is purchased, and it does not have a spare tire. What is the probability that the car was produced at plant B?

Conditional Probabilities - Calculators - from 3.4

Josh has an IU calculator and a Purdue calculator. The IU calculator gives the correct answer 75% of the time, while the Purdue calculator gives the right answer 50% of the time. Josh chooses a calculator randomly and type in 1+1. The calculator says 3. What’s the probability that it was a Purdue calculator?

Bernoulli Coin Toss - from 3.5

An unfair coin with Pr(H) = 0.6 is flipped 3 times and the result of each toss is noted. What is the probability that there are at least two heads?