1. A fair, 10 sided die is rolled. Find the probability that
a. the number rolled was less than 5, given that the number rolled was even
b. the number rolled was a multiple of 4, given that the number was less than 7
2. A professor has noticed that even though attendance is not a component of the grade for his class, students who
attend regularly obtain better grades. In fact, the probability of attending regularly and receiving an A is 40%, while the
probability of not attending regularly and receiving an A is 10%. The probability of attending class regularly is 70%. Find
the probability of
a. a student receiving an A given they attend class regularly
b. a student receiving an A given they do not attend class regularly
3. A Basket of fruit is on your kitchen table containing 3 oranges, 1 apple, and 5 bananas. If two pieces of fruit are
selected randomly, without replacing, find the probability of choosing
a. 2 oranges
b. a banana and then an orange
c. an apple and an orange in any order
4. A bag contains 2 blue marbles and 5 red marbles. Consider drawing marbles without replacing them and find the
probability of drawing
a. a red marble first and a blue marble second
b. two blue marbles
5. A sock is pulled from your drawer containing 6 black socks, 4 seasonal socks, and 2 white socks. Find the probability
that a sock is pulled at random and is
a. either a black or white sock
b. neither a black nor a white sock
6. a. What is the probability of flipping 6 tails in a row on a fair two sided coin?
b. How many answer keys are there to a 15 question multiple choice test if there are 3 possible answers for each
questions?
7. Jill is playing cards and draws a card from a pack of cards numbered 1 to 20.
a. What is the probability of drawing a number that is a square?
b. what is the probability of drawing a number that is a multiple of 3 or a multiple of 5 (be careful not to count the same
number twice)
8. a. How many ways can you rearrange the letters in THE TWO TOWERS to make new distinguishable words?
b. How many ways can you rearrange the letter in BATTLE OF THE FIVE ARMIES to make new distinguishable words?
9. The Athletic Council decides to form a sub-committee of seven members to look at how funds raised should be spent
on sports activities at the school. There are a total of 15 council members, 9 of which are male and the rest are female.
a. What is the probability that the sub-committee will consist of exactly 3 females?
b. what is the probability that the sub-committee will consist solely of males?
10. A bag of marbles contains 5 red, 3 green and 6 blue marbles. If a child grabs three marbles from the bag, determine
the probability that
a. exactly 2 are blue
b. at least on is blue
c. the first one is red, the second is green and the third is blue
d. one is red, one is green and one is blue
11. Three prizes are awarded in a raffle during the halftime show at a school basketball game. You and 19 other students
have bought a ticket for $3. If there is one $25 gift card and two $10 gift cards find the expected value for this raffle and
determine if you made a good choice to buy a ticket.
12. A company makes electronic gadgets. A batch of gadgets consists of 50 total gadgets. One out of every batch is
faulty, but the company cannot determine if it is defective until a buyer complains. Suppose the company makes $3
profit on the sale of each working gadget, but spends $80 to fix each faulty gadget.
a. What is the expected profit per gadget?
b. What is the expected profit for producing 100 batches of gadgets?