Section 2.8Probability and Odds

Objectives: Find the probability of an event

Find the odds of an event

Terms

Probability of an event: a measure of the likelihood that the event will occur due to chance. It is a number between 0 and 1, inclusive

Outcomes: the different possible results of a probability experiment

Event: a collection of outcomes

Theoretical probability: a type of probability that is based on the number of favorable outcomes divided by the total number of outcomes

Favorable outcomes: the outcomes for a particular event that are being considered

Experimental probability: a probability that is based on repetitions of an actual experiment

Odds: the ratio of the number of ways an event can occur to the number of ways the event cannot occur

Examples

1. In a group of students, 12 ride the bus to school, 8 are driven to school and 5 walk. One of the students is chosen at random from the group. What is the probability P that the student walks to school?

2. Last January it snowed 7 days, was sunny 18 days and was cloudy 6 days. Based on this information, what is the probability that it will snow on a randomly chosen day in January?

Experimental probability directions

With a partner toss three coins 20 times and record the number of heads for each of the 20 tosses.

a) Use your results to find the experimental probability of getting three heads when three coins are tossed.

b) Combine your results with those of all the other pairs in your class. Then use the combined results to find the experimental probability of getting three heads when three coins are tossed.

c) Find the theoretical probability of getting three heads when three coins are tossed? How does it compare with your results from b?

Coin Toss Experiment Results

Combo Tally #1 Tally #2

HHH

HTT

HHT

HTH

THH

TTH

THT

TTT

TOTAL

a) P(HHH) =

b) P(HHH) =

c) P(HHH) =

Example of a survey

Salary Type of company

Size of company

Location

93 37 17 103

3. Use the table showing the responses of college students to a survey asking “Which factor is most likely to influence your job choice after graduation?’ If you were to ask a randomly chosen college student this question, what is the experimental probability that the student would say “type of company”?

Odds

4. You randomly choose a letter from the word SUMMER. What are the odds that the letter is a vowel?

What are the odds that the letter is a M?

5. The probability that a randomly chosen 4 digit security code contains at least one zero is 0.34. What are the odds that a 4 digit security code contains at least one zero?

p. 11710 – 22 evens, 28 – 30 all,

33, 34, 46 – 56 evens