Probability of Independent Events

1
Pre-Calculus Review for Quiz (Probability)
Name________________________________ Date_______
__________________________
Probability of the Union of Two Events
P(A or B) P(A) P(B) P(A n B)
Probability of Independent Events P(A and B)
P(A) P(B)
The complement of A is written A' . P(A') 1
P(A)
1. From a group consisting of 4 people (Allen,
Bob, Carol and Donna), two people are to be
randomly selected to serve on a committee.
a. What is the sample space for this?
b. What is the probability that Bob and Carol
are selected. c. What is the probability
that Carol is not selected?
2. You roll two eight-sided dice whose sides are
each numbered 1 through 8. What sum has the
highest probability of occurring?
3. Suppose the odds in favor of the Downtown
Bears beating the Crosstown Cubs in a softball
game are 4 to 3. a. What is the
probability that the Bears win? b. What is the
probability that the Cubs win?
4. The letters of the word TEXAS are arranged in
random order. What is the probability that the
letters spell TAXES?
5. A number between 100 and 999, inclusive, is
chosen at random. What is the probability
that a. it contains no zeros? b. it contains at
least one zero?
6. Two yellow marbles and three greens marbles
are placed in a bag. One marble is chosen, then
replaced, and then a second marble is
chosen. a. Find the probability that both
marbles chosen were the same color. b. What is
the probability that both are the same color if
there was not replacement?
7. In a survey of 1000 students in a school, 950
indicated that they were right-handed. If four
students are selected randomly from the 1000
students, what is the probability that at least
one is left-handed?
8. What is the probability of getting a full
house when playing poker with a standard deck of
52 cards?
2
Pre-Calculus Review for Quiz Answer Sheet
1. sample space consists of 6 items (
) order doesnt matter
Allen Bob Bob Carol
Allen Carol Bob Donna
Allen Donna Carol Donna b.
? c. ?
2. 9 3. a. b.
4. 120 different ways to arrange
the letters , so
5. There are 900 different numbers 9 x 10 x
10 a.
b. 1 P(no zeros)

• a. P(both same color) P(YY or GG) P(YY)
  P(GG)
• b. P(both same color without
  replacement)

7. P(at least one left-handed) 1 P(all
right handed) 1 (.95)4 .185
8. Remember 3744 is the number of ways to get a
full house. So the probability is the ratio of
this number over the total number of 5
cards hands.