Here are questions related to probability completed with the answers and explanations.
(If you have other questions related to probability, please post your question as a reply to this thread)

In a workshop there are 4 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
The answer and explanation

Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart." If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
The answer and explanation

Three people are to be seated on a bench. How many different sitting arrangements are possible if Erik must sit next to Joe?
The answer and explanation

Barbara has 8 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?
The answer and explanation

A credit card number has 5 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?
The answer and explanation

How many 3-digit numbers satisfy the following conditions: The first digit is different from zero and the other digits are all different from each other?
The answer and explanation

If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include 2 people who are married to each other, how many such committees are possible?
The answer and explanation[spoiler=][1] Total combinations = ₁₀c₃ = 120
[2] Total combinations which include atleast one couple = 5 * 8 = 40

one couple can be chosen among the 5 couples in 5 ways. the remaining one slot can be filled with any one of the 8 people remaining in 8 ways

Total combinations which do not include any couple = [1] - [2] = 80

As another approach, total combinations = (total permutations)/n! = 10 * 8 * 6 / 3! = 480 / 6 = 80[/spoiler]

A bag contains five red balls, four black, and six green. Two balls are selected at random without replacing them to the bag. What is the probability that a red ball and a black ball will be selected?
The answer and explanation