3.1 – Probability and Odds3.1 – Probability and Odds

3.1 – Probability and Odds3.1 – Probability and Odds

Today we will be learning about:Today we will be learning about: Finding the probability of an eventFinding the probability of an event

Finding the odds of an eventFinding the odds of an event

3.1 – Probability and Odds3.1 – Probability and Odds

Probability of an event – measure of the likelihood that the event will occur. It is a number between 0 and 1

3.1 – Probability and Odds3.1 – Probability and Odds

Outcomes – different possible results When an event has N equally likely outcomes,

each of them occur with probability 1/N. Example: Rolling a six-sided number cube, the

possible outcomes are 1, 2, 3, 4, 5, and 6. The probability associated with each outcome is 1/6.

3.1 – Probability and Odds3.1 – Probability and Odds

EVENT – all of the possible outcomes In the roll of a six-sided number cube, an “even

roll” consists of the outcomes 2, 4, and 6. THEORETICAL PROBABILITY - the

probability that should happen. The theoretical probability of an even roll is 3/6 =

½. FAVORABLE OUTCOMES – the outcomes

you wish to have happen.

3.1 – Probability and Odds3.1 – Probability and Odds

Theoretical Probability P =

Number of favorable outcomes

Total number of outcomes

3.1 – Probability and Odds3.1 – Probability and Odds

Another type of probability is EXPERIMENTAL PROBABILITY. This type of probability is based on repetitions of an actual experiment and is calculated by the following rule.

Experimental probability P = Number of favorable outcomes observed

Total number of trials

3.1 – Probability and Odds3.1 – Probability and Odds

Example 1 You have 2 red and 2 black socks in a drawer.

You reach in and pick two without looking. What is the probability P that they do not match

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?

3.1 – Probability and Odds3.1 – Probability and Odds

Example 2 Use the circle graph below showing the responses of 250

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?”

Salary-93

location-103

Type of company37

Size of company

17

3.1 – Probability and Odds3.1 – Probability and Odds

THE ODDS OF AN EVENT When all outcomes are equally likely, the ODDS

that an event will occur are given by the formula: ODDS = Number of favorable outcomes

Number of unfavorable outcomes

3.1 – Probability and Odds3.1 – Probability and Odds

Example 3 You randomly choose a letter from the word

SUMMER. What are the odds that the letter is a vowel?

3.1 – Probability and Odds3.1 – Probability and Odds

Example 4 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?

3.1 – Probability and Odds3.1 – Probability and Odds

Ex.5 – Given the odds, find the probability.Ex.5 – Given the odds, find the probability. The odds of rolling a number greater than 2, on a die, are 2:1. The odds of rolling a number greater than 2, on a die, are 2:1.

What is the probability of rolling a number greater than 2?What is the probability of rolling a number greater than 2? Probability of event occurring = [left side of odds/(left side of Probability of event occurring = [left side of odds/(left side of

odds + right side of odds)]odds + right side of odds)]

= 2/(2 + 1) = 2/3= 2/(2 + 1) = 2/3

Probability of event not occurring = [right side of odds/(left Probability of event not occurring = [right side of odds/(left side + right side)] = side + right side)] =

1 – (probability of the event occurring)1 – (probability of the event occurring)