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### Statistics

### Statistics

### Statistics

### Statistics

### Statistics

### Statistics

Probability - Simple Probability and Odds

Math Pacing- Which measure of central tendency best describes the data? Explain.

Mean: 3.1, Median: 3.6, Mode:1.1

78, 82, 85, 86, 87, 88, 88, 88, 89, 89, 90, 92, 95, 98, 98

WS 2-5 Practice #3, 4, 6 – 10 (7 problems – 17 points)

Probability - Simple Probability and Odds

One way to describe the likelihood of an event occurring is with probability.

The probability of a simple event, like a coin landing heads up when it is tossed, is a ratio of the number of favorable outcomes for the event to the total number of possible outcomes of the event.

The probability of an event can be expressed as a fraction, a decimal, or a percent.

Probability - Simple Probability and Odds

Suppose you wanted to find the probability of rolling a 4 on a die.

When you roll a die, there are six possible outcomes, 1, 2, 3, 4, 5 or 6.

This list of all possible outcomes is called the sample space.

Of these outcomes, only one, a 4, is favorable.

So the probability of rolling a 4 is:

Probability - Simple Probability and Odds

REPEAT: The probability of a simple event is a ratio of the number of favorable outcomes for the event to the total number of possible outcomes of the event.

The probability of an event a can be expressed as:

6 possibleoutcomes

Answer:

Find Probabilities of Simple Events

Example 6-1aFind the probability of rolling a number greater than 2 on a die.

There are six possible outcomes. Four of the outcomes are favorable. That is, four of the six outcomes are numbers greater than two.

Sample space: 1,2,3,4,5,6

number of possible outcomes

Simplify.

Answer: The probability of selecting a student with black hair is

Find Probabilities of Simple Events

Example 6-1bA class contains 6 students with black hair, 8 with brown hair, 4 with blonde hair, and 2 with red hair. Find P(black).

Thereare 6 students with black hair and 20 total students.

number of possible outcomes

Answer:The probability of selecting a student with redor brown hair is

Simplify.

Find Probabilities of Simple Events

Example 6-1cA class contains 6 students with black hair, 8 with brown hair, 4 with blonde hair, and 2 with red hair. Find P(red or brown).

Thereare 2 students with red hair and 8 students with brown hair. So there are 2 + 8 or 10 students with red or brownhair.

number of possible outcomes

Simplify.

Answer: The probability of selecting a student who doesnot have blonde hair is

Find Probabilities of Simple Events

Example 6-1eA class contains 6 students with black hair, 8 with brown hair, 4 with blonde hair, and 2 with red hair. Find P(not blonde).

There are 6 + 8 + 2 or 16 students who do not have blonde hair.

Answer:

Find Probabilities of Simple Events

Example 6-1fa. Find the probability of rolling a number less than 3 on a die.

b. A gumball machine contains 40 red gumballs, 30 green gumballs, 50 yellows gumballs, and 40 blue gumballs. Find P(red).

Answer:

Find Probabilities of Simple Events

Example 6-1gc. A gumball machine contains 40 red gumballs, 30 green gumballs, 50 yellows gumballs, and 40 blue gumballs. Find P(green or yellow).

d. A gumball machine contains 40 red gumballs, 30 green gumballs, 50 yellows gumballs, and 40 blue gumballs. Find P(not blue).

Probability - Simple Probability and Odds

You should have noticed that the probability that an event will occur is somewhere between 0 and 1 (or 0% and 100%) inclusive.

If the probability of an event is 0, that means that it is impossible for the event to occur.

A probability equal to 1 means that the event is certain to occur.

There are outcomes for which the probability is ½.

When this happens, the outcomes are equally likely to occur or not to occur.

Probability - Simple Probability and Odds

Another way to express the chance of an event occurring is with odds.

The odds of an event occurring is the ratio that compares the number of ways an event can occur (successes) to the number of ways it cannot occur (failures).

ODDS

successes : failures

4:2

2 numbers less than orequal to 2

Odds of an Event

Example 6-2aFind the odds of rolling a number greater than 2.

There are six possible outcomes, 4 are successes and 2 are failures.

Sample space: 1,2,3,4,5,6

Answer:The odds of rolling a number greater than 2 are 4:2 or 2:1.

Example 6-2b

Find the odds of rolling a number less than 4.

Sample space: 1,2,3,4,5,6

Answer: 3:3 or 1:1

Probability - Simple Probability and Odds

The odds AGAINST an event occurring are the odds that the event will NOT occur.

number of ways not to picka 2 or 3

odds against a 2 or 3 = 44:8

number of ways to picka 2 or 3

Odds Against an Event

Example 6-3aA card is selected at random from a standard deck of 52 cards. What are the odds against selecting a 2 or 3?

There are four 2s and four 3s in a deck of cards, and there are 52 – 4 – 4 or 44 cards that are not a 2 or a 3.

Answer:The odds against selecting a 2 or 3 are 11:2.

Example 6-3b

A card is selected at random from a standard deck of 52 cards. What are the odds against selecting a 5, 6, or 7?

Answer: 10:3

odds of the plane being on time

Probability and Odds

Example 6-4aTravel Melvin is waiting to board a flight to Washington, D.C. According to the airline, the flight he is waiting for is on time 80% of the times it flies. What are the odds that the plane will be on time?

The probability that the plane will be on time is 80%, so the probability that it will not be on time is 20%.

Answer: The odds that the plane will be on time are 4:1.

Example 6-4b

If the probability that it will snow this weekend is 70%, what are the odds that it will snow?

Answer: 7:3

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