1. Probability
The risk of getting struck by lightning in any year is 1 in 750,000. The chances of surviving a lightning strike are 3 in 4. These risks and chances are a way of describing the probability of an event.
The probability of an event is a ratio that measures the chances of the event occur.

2. Introduction to Probability
The Probability of an event occurring is a number between 0 and 1.
0 means that the event cannot occur…
1 means that the event is certain to occur.
The probability that event A will occur is
P(A) = number of outcomes in A total number of outcomes

3. P(3)= P(prime #)= P(factors of 8)= P(9)= 1 2 3 4 5 6 7 8
Quick Examples of Probability: 1 2 3 4 5 6 7 8
P(3)=
P(prime #)=
P(factors of 8)=
P(9)=

4. Ex1:
a. Four cards are drawn from a standard 52-card deck. What
is the probability that the first three cards are black?
b. Five cards are drawn from a standard 52-card deck. What
is the probability that the first five cards are spades?

5. Roman has a collection of 26 books–16 are fiction and 10 are nonfiction. He randomly chooses 8 books to take with him on vacation. What is the probability that he chooses 4 fiction and 4 nonfiction?
Step 1 Determine how many 8-book selections meet the conditions. C(16, 4) Select 4 fiction books. Their order does not matter.
C(10, 4) Select 4 nonfiction.

6. Answer: The probability is about 0.24464 or 24.5%.
Example 3-2a

7. Another way to measure the chance of an event occurring is with odds.
Odds: The odds that an event will occur can be expressed as the ratio of the number of successes to the number of failure.
Odds of success = s : f

8. a. What are the odds that a male born in 1980 will live to age 65?
Example 3
Life Expectancy The chances of a male born in 1980 to live to be at least 65 years of age are about 7 in 10. For females, the chances are about 21 in 25.
a. What are the odds that a male born in 1980 will live to age 65?
b. What are the odds that a female born in 1980 will live to age 65?
Answer: 7:3
Answer: 21:4
Example 3-3b

9. Many experiments, such as rolling a die, have numerical outcomes.
A random variable is a variable whose value if the numerical outcome of a random event.
For example, when rolling a die we can let the random variable D represent the number showing on the die.
Thus, D can equal 1, 2, 3, 4, 5, or 6.
A probability distribution, for a particular random variable is a function that maps the sample space to the probabilities of the outcomes in the sample space.

10. The following is the probability distribution for rolling a die.
D = Roll 1 2 3 4 5 6
Probability
Further, to help visualize a probability distribution, you can a graph, called a relative-frequency histogram.

11. Relative-frequency histogram
Suppose two dice are rolled. The table and the relative-frequency histogram show the distribution of the sum of the numbers rolled.
Probability 12 11 10 9 8 7 6 5 4 3 2
S = Sum
Example 3-4a

12. Relative-frequency histogram
Use the graph to determine which outcomes are least likely. What are their probabilities?
Answer: The least probability is The least likely outcomes are sums of 2 and 12.
Example 3-4a

13. Use the table to find What other sum has the same probability.12 11 10 9 8 7 6 5 4 3 2
S = Sum
Use the table to find What other sum has the same probability.
Answer: The other sum with this probability is a sum of 3.
Example 3-4a

14. What are the odds of rolling a sum of 5?
Step 1
Identify s and f.
Step 2
Find the odds.
Answer: So, the odds of rolling a sum of 5 are 1:8.
Example 3-4a