Dear Family,

©Curriculum Associates, LLC Copying is not permitted. 331Lesson 32 Probability Models

The experimental probability of an event occurring is based on actual results from an experiment. The theoretical probability of an event occurring is what you would expect to happen in an experiment.

Here’s an example of each kind of probability.

• You would expect a coin to land on heads half the times that the

coin is tossed. The theoretical probability of heads is 1 ··

2 .

• You actually toss a coin 10 times and it lands on heads 7 times.

The experimental probability of heads is 7 ··

10

.

Experimental probability and theoretical probability do not always give the same results. However, the more trials you do in an experiment, the closer the experimental probability will be to the theoretical probability.

Consider the following example:

A family has two boys. The family tossed a coin to represent the likelihood of a boy if they have another child. They used heads to represent a boy and tails to represent a girl. The table below shows the results of their experiment. If the family has another child, predict whether the child will be a boy.

Coin Toss Tally Total

Heads (boy) IIII I 6

Tails (girl) IIII IIII IIII 14

On the next page you will see ways your child may find the experimental probability and the theoretical probability of whether the child will be a boy.

Use with Ready Instruction Lesson 32

Your child is learning about probability models.

©Curriculum Associates, LLC Copying is not permitted.332 Lesson 32 Probability Models

Probability Models: Sample Solution

A family with two boys tossed a coin to represent the likelihood of a boy if they have another child. Heads represents a boy and tails represents a girl. The table below shows the results of their experiment. If the family has another child, predict whether the child will be a boy.

Coin Toss Tally Total

Heads (boy) IIII I 6

Tails (girl) IIII IIII IIII 14

Describe the sample space, or all of the possible outcomes for the experiment. There are two possible outcomes: the family will either have a boy or a girl. These outcomes are equally likely.

In this case you want to find the probability that the family has a boy. Compare the experimental probability to the theoretical probability.

Experimental probability of a boy:

P(boy) 5 number of heads ·············

number of trials

5 6 ··

20

The experimental probability of a boy is 6 ··

20

, or 3 ··

10

.

Theoretical probability of a boy: Total number of possible outcomes: 2 (boy or girl) Favorable outcomes: 1 (boy)

P(boy) 5 number of favorable outcomes ·······················

number of possible outcomes

5 1 ··

2

The theoretical probability of a boy is 1 ··

2 .

Answer: The experimental probability of having a boy is 3 ··

10

and the

theoretical probability of having a boy is 1 ··

2 . Based on the experimental

probability, you would predict a boy only 3 ··

10

of the time. Based on the

theoretical probability, you would predict a boy 1 ··

2 of the time.