Download Section 8.2

Section 8.2 Outcomes with Unequal Probability; Odds
General Rules for Probability
If a sample space, S, has a finite number of outcomes then:
1) The probability of each outcome is between 0 and 1 inclusive
2) The sum of the probabilities of all outcomes = 1
3) The probability of the empty set = 0
The probability of a particular event in S is found by adding the probabilities of all outcomes making up
that event.
Example:
#10 Spinners
The arrow on the spinner in the given figure is spun, and the letter representing the area the arrow
points to is then recorded.
a)
Find the sample space for this experiment, and assign probabilities to each outcome of the
sample space.
b) What is the probability that the arrow will point to the area labeled A or the area labeled D?
c) What is the probability that the arrow will point to the area labeled B or the area labeled C?
#14 Eight red, five green, seven blue, and ten purple balls are in a box One ball is to be randomly drawn
from the box and the color recorded.
a.
Find the sample space for this experiment, and assign probabilities to each outcome of the
sample space.
b. What is the probability that the ball is red or green?
c. What is the probability that the ball will not be red?
#34 Two cards are to be dealt, without replacement, from a deck of 52 cards, and the number of clubs
is to be recorded.
a.
Find the sample space for this experiment and the probability of each outcome of that sample
space.
b. Find the probability that at least one club will be dealt.
c. Construct the probability distribution for this experiment.
Up to this point the probabilities that we have found have been based on theory. In some instances,
however, we are more likely to base our probabilities on collection of samples. When we base our
probabilities on actual physical experimentation we are assuming the relative frequencies that we
observe are valid for an entire population even though they are only approximations. These relative
frequency assignments are called empirical probabilities because they are based on empirical evidence.
#43 A survey of 120 economists shows that 64 predict a recession, 42 predict that the economy will
show slow growth, and 14 predict sharply higher growth within the next year.
a. Make an empirical probability distribution for this information.
b. Based on the given information, find the probability that there will be no recession within the
next year.
ODDS: Let E be an event in a sample space S where E is not all of S. Then the odds for E are found by
reducing P(E)/P(E’) to lowest terms a/b and writing “a to b” or “a:b”. Similarly, the odds against E are
found by reducing P(E’)/P(E) to lowest terms.
#54 A pair of dice, one red and one green, is to be rolled. Find the odds
a) For the card being a king
b) Against the card being a club.