math pacing probability - simple probability and odds 1.which measure of central tendency best...

Probability - Simple Probability and Odds

1. Which measure of central tendency best describes the data? Explain.

2.

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

Mean: 3.1, Median: 3.6, Mode:1.1


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.


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: %17about or 61.0,61


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:

outcomes possible ofnumber total

outcomes favorable ofnumber aP

Find 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

4 numbers greater than 2

6 possibleoutcomes

Answer:

Find Probabilities of Simple Events

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

There are 6 students with black hair and 20 total students.

number of favorable outcomes

number of possible outcomes

Answer: The probability of selecting a student with black

hair is

Simplify.


A 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). There are 2 students with red hair and 8 students with brown hair. So there are 2 + 8 or 10 students with red or brown hair.



Simplify.


Answer: The probability of selecting a student with red

or brown hair is

A 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.



Simplify.

Answer: The probability of selecting a student who does

not have blonde hair is


a. 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:

Answer:


c. 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).

Answer:

Answer:



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.


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

Find 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

4 numbers greater than 2

2 numbers less than orequal to 2

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

Odds of an Event

4:2

Find the odds of rolling a number less than 4.

Answer: 3:3 or 1:1

Odds of an Event

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


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

A 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.

Odds Against an Event

number of ways not to picka 2 or 3

number of ways to picka 2 or 3

odds against a 2 or 3 = 44:8

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 Against an Event

Travel 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%.

odds of the plane being on time

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

Probability and Odds

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

Answer: 7:3

Probability and Odds

math pacing probability - simple probability and odds 1.which measure of central tendency best...

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