Math 310 Final Exam Practice Questions
A. Probability
1. A fair coin was flipped 5 times and landed heads five times. What is the probability of a head
on the next toss?
2. One card is selected at random from an ordinary deck of 52 cards. Find the probability of
each of the following events.
(a) A spade is drawn.
(b) The king of spades is drawn.
(c) A heart or a face card is drawn.
(d) The two of clubs is not drawn.
3. A box contains three blue cards and four white cards. Two cards are drawn one at a time.
(a) Find the probability that both cards are blue if the draws are made with replacement.
(b) Find the probability that both cards are blue if draws are made without replacement.
(c) Draw a tree diagram for the experiment in part (b), complete with all probabilities.
4. In firing a NASA three-stage rocket, the probability of the success of stage 1 is 95%, of stage
2, 97%, and of stage 3, 98%. Assuming that the stages are independent, what is the probability
for success in all three stages during a single launch?
5. (a) If the odds in favor of the Dodgers winning the game are 8 to 5, what is the probability
that they will win?
(b) If the probability our team will win is 2/5, what are the odds against our team?
6. Two standard dice are rolled. What are the odds in favor of rolling a sum of 3?
7. The English names of the months of the year are placed in a hat and one is drawn at random.
(a) List the sample space for this experiment.
(b) List the event consisting of the outcomes that the month drawn starts with the letter J.
(c) What is the probability of drawing the name of a month that starts with J?
8. (a) If P(A) = 2/3, P(B) = 1/2, and P(B|A) = 1/3, find P(A|B).
(b) If two-thirds of the books in the library are new, and half of the books in the library are
non-fiction, but only one-third of the new books are non-fiction, find the probability that a book
selected at random from the library is new, given that it is a non-fiction book.
9. Sara has a collection of 7 books: War and Peace, Steppenwolf, One Hundred Years of
Solitude, Huckleberry Finn, Lord of the Flies, The Old Man and the Sea, The Grapes of Wrath.
If she randomly selects three of her books to read in sequence this month, what is the probability
that she will read War and Peace, Steppenwolf, and One Hundred Years of Solitude in that
order?
