Download Putting It All Together

Conditional Probability
Name:_______________________________ Pd:______ #
You must justify each probability by listing possible outcomes or showing/explaining your method of
counting.
1. A class contains 10 men and 20 women of which half of the men and half of the women have brown
eyes. Find the probability that a person chosen at random is a man or has brown eyes.
Eye Color/Gender Men Women
Brown
5
10
Other
5
10
P( man or has brown eyes) =
2. Suppose a couple has two children. The sample space S = {bb, bg, gb, gg}. We will assume each
outcome has an equal probability. Find the probability that both children are boys if it is known that
a. At least one of the children is a boy
New Sample Space: S =
P( both boys | at least one boy) =
b. The first child is a boy
P( both boys | first child is a boy) =
New Sample Space: S =
3. Three fair coins a penny, a nickel, and a dime are tossed.
Sample Space: S =
Find the probability p that they are all heads if:
a. The penny is heads. P( all heads | penny is heads) =
b. At least one of the coins is heads. P( all heads |
c. The dime is tails. P(all heads |
4. A pair of fair dice is thrown. Find the probability that the sum is 10 or greater if:
a. 5 appears on the first die.
New Sample Space: S =
P(
b. 5 appears on at least one die.
P(
New Sample Space: S =
Math
5. Complete the Venn Diagram to help you answer the questions.
In a certain college, 25 percent of the students failed mathematics, 15
percent failed chemistry and 10 percent failed both math and chemistry.
A student is selected at random.
a. If the student failed chemistry, what is the probability that he or she
failed math?
P( failed math | failed chem) =
Chem
b. If the student failed math, what is the probability that he or she failed
chemistry?
c. What is the probability that the student failed math or chemistry?
d. What is the probability that the student failed neither math nor chemistry?
6. A box contains 7 red marbles and 3 white marbles. Three marbles are drawn from the box one after the
other. Find the probability that the first 2 are red and the third is white.
7. A pair of fair dice is tossed. If the faces appearing are different.
a. The sample space for this problem does not contain 36 possible outcomes. Why?
b. Find the probability the sum is even given the faces appearing are different.
c. Find the probability the sum exceeds nine given the faces appearing are different.
8. Three cards are drawn in succession (without replacement) from a 52-card deck. Find the probability
that
a. All three are aces.
b. If the first is an ace then the other two are aces
c. If the first two are aces then the third is an ace