warm up 1. what is the probability of getting two tails if two coins are tossed? 2. give the...

Warm Up

1. What is the probability of getting two tails if two coins are tossed?

2. Give the probability that the roll of a number cube will show 1 or 4.

3. Give the expected number of rolls that will result in a 2 if a number cube is rolled 42 times.

14

13

7

Course 2

10-4 Theoretical Probability

Learn to find the theoretical probability of an event.

Course 2


Vocabulary

favorable outcometheoretical probabilityfair

Insert Lesson Title Here

Course 2


Theoretical Probability

In the game of Scrabble®, players use tiles bearing the letters of the alphabet to form words. Of the 100 tiles used in a Scrabble game, 12 have the letter E on them. What is the probability of drawing an E from a bag of 100 Scrabble tiles?

Course 2


Theoretical Probability

In this case, pulling an E from the bag is called a favorable outcome. A favorable outcome is an outcome that you are looking for when you conduct an experiment.

To find the probability of drawing an E, you can draw tiles from a bag and record your results, or you can find the theoretical probability. Theoretical probability is used to estimate the probability of an event when all the outcomes are equally likely.

Course 2


If each possible outcome of an experiment is equally likely, then the experiment is said to be fair. Experiments involving number cubes and coins are usually assumed to be fair.

You can write probability as a fraction, a decimal, or a percent.

THEORETICAL PROBABILITY

probability = number of favorable outcomestotal number of possible outcomes

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Find the probability. Write your answer as a fraction, as a decimal, and as a percent

Additional Example 1A: Finding Theoretical Probability

A. Andy has 20 marbles in a bag. Of these, 9 are clear. What is the probability of drawing a clear marble from the bag?

P = number of favorable outcomes total number of possible outcomes

P(clear) = number of clear marblestotal number of marbles

= 920

= 0.45 = 45%

The theoretical probability of drawing a clear marble is , 0.45, or 45%.920

Write the ratio.

Substitute.

Write as a decimal and write as a percent.

Course 2


B. What is the probability of rolling a number less than 4 on a fair number cube.

Additional Example 1B: Finding Theoretical Probability

For a fair number cube, each of the six possible outcomes is equally likely. There are 3 ways to roll a number less than 4: 1, 2, or 3.


P(number less than 4) = 3 numbers less than 46 possible outcomes

= 36

= 12

= 0.5 = 50%The theoretical probability of rolling a number less than 4 is 0.50, or 50%. 12 ,

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Find the probability. Write your answer as a fraction, as a decimal, and as a percent.


P(green) = number of green marblestotal number of marbles

= 820

= 0.4 = 40%

The theoretical probability of drawing a green marble is , 0.4, or 40%.820

Write the ratio.

Substitute.

Write as a decimal and write as a percent.

Try This: Example 1A

A. Jane has 20 marbles in a bag. Of these 8 are green. What is the probability of drawing a green marble from the bag?

Course 2


B. What is the probability of rolling a number more than 4 on a fair number cube.


P(number more than 4) = 2 numbers more than 4 6 possible outcomes

= 26

= 13

0.33 33%The theoretical probability of rolling a number more than 4 is 0.33, or 33%. 13 ,

Try This: Example 1B

For a fair number cube, each of the six possible outcomes is equally likely. There are 2 ways to roll a number greater than 4: 5 or 6.

Course 2


The coach has written the names of each of the track team members on an index card. She draws randomly from these cards to choose a student to run a sprint and then replaces the card in the stack.

Additional Example 2A: School Application

A. If there are 13 boys and 10 girls on the team, what is the theoretical probability that a girl’s name will be drawn?

=1023

Find the theoretical probability.Substitute.

P(girl) = number of girls on the teamnumber of members on the team

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Additional Example 2B: School Application

The coach has written the names of each of the track members on an index card. She draws randomly from these cards to choose a student to run a sprint and then replaces the card in the stack.

B. If there are 13 boys and 10 girls on the team, what is the theoretical probability that a

boy’s name will be drawn?

= 1323

Find the theoretical probability.

Substitute.

P(boy) = number of boys on the team number of members on the team

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Try This: Example 2A


A teacher has written the name of each student on a piece of paper and placed the names in a box. She randomly draws a paper from the box to determine which student will present the answer to the problem of the day.

A. If there are 15 boys and 12 girls in the class, what is the theoretical probability that a girl’s name will be drawn?

=1227


Substitute.

P(girl) = number of girls in the classnumber of students in the class

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Try This: Example 2B


= 1527


Substitute.

B. If there are 15 boys and 12 girls in the class, what is the theoretical probability that a

boy’s name will be drawn?

P(boy) = number of boys in the classnumber of students in the class

Course 2


A teacher has written the name of each student on a piece of paper and placed the names in a box. She randomly draws a paper from the box to determine which student will present the answer to the problem of the day.

Lesson QuizFind the probabilities. Write your answer as a fraction, as a decimal to the nearest hundredth, and as a percent to the nearest whole percent. You have 11 cards, each with one of the letters from the word mathematics.

1. Find the probability of drawing an m from the pile of shuffled cards.

2. Find the probability of drawing a vowel. 3. Find the probability of drawing a consonant. 7

11

211


4 11

, 0.18, 18%

, 0.36, 36%

, 0.64, 64%

Course 2


warm up 1. what is the probability of getting two tails if two coins are tossed? 2. give the...

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