Chance Experiments with Outcomes that are Not Equally Likely

Examples, videos, and solutions to help Grade 7 students learn how to to calculate probabilities for chance experiments that do not have equally likely outcomes.

New York State Common Core Math Grade 7, Module 5, Lesson 5

Worksheets for Grade 7

Lesson 5 Student Outcomes

• Students calculate probabilities for chance experiments that do not have equally likely outcomes.

Lesson 5 Summary

• In a probability experiment where the outcomes are not known to be equally likely, the formula for the probability of an event does not necessarily apply.
For example:
• To find the probability that the score is greater than 3, add the probabilities of all the scores that are greater than 3.
• To find the probability of not getting a score of 3, calculate 1 – (the probability of getting a 3).

Lesson 5 Classwork

In previous lessons, you learned that when the outcomes in a sample space are equally likely, the probability of an event is the number of outcomes in the event divided by the number of outcomes in the sample space. However, when the outcomes in the sample space are not equally likely, we need to take a different approach.

Example 1
When Jenna goes to the farmer’s market she usually buys bananas. The numbers of bananas she might buy and their probabilities are shown in the table below.
a. What is the probability that Jenna buys exactly 3 bananas?
b. What is the probability that Jenna doesn’t buy any bananas?
c. What is the probability that Jenna buys more than bananas?
d. What is the probability that Jenna buys at least bananas?
e. What is the probability that Jenna doesn’t buy exactly bananas?
Notice that the probabilities in the table add to 1. This is always true;
when we add up the probabilities of all the possible outcomes, the result is always 1. So, taking and subtracting the probability of the event gives us the probability of something NOT occurring.

Exercises 1–2
Jenna’s husband, Rick, is concerned about his diet. On any given day, he eats 0, 1, 2, 3, or 4 servings of fruit and vegetables. The probabilities are given in the table below.

1. On a given day, find the probability that Rick eats:
   a. Two servings of fruit and vegetables.
   b. More than two servings of fruit and vegetables.
   c. At least two servings of fruit and vegetables.
   
2. Find the probability that Rick does not eat exactly two servings of fruit and vegetables.

Example 2
Luis works in an office, and the phone rings occasionally. The possible numbers of phone calls he receives in an afternoon and their probabilities are given in the table below.
a. Find the probability that Luis receives or phone calls.
b. Find the probability that Luis receives fewer than phone calls.
c. Find the probability that Luis receives or fewer phone calls.
d. Find the probability that Luis does not receive phone calls.

Exercises 3–6
When Jenna goes to the farmer’s market, she also usually buys some broccoli. The possible number of heads of broccoli that she buys and the probabilities are given in the table below.
Find the probability that Jenna:
3. buys exactly heads of broccoli.
4. does not buy exactly heads of broccoli.
5. buys more than head of broccoli.
6. buys at least heads of broccoli.

Exercises 7–10
The diagram below shows a spinner designed like the face of a clock. The sectors of the spinner are colored red (R), blue (B), green (G), and yellow (Y).
Spin the pointer, and award the player a prize according to the color on which the pointer stops.
7. Writing your answers as fractions in lowest terms, find the probability that the pointer stops on
a. red:
b. blue:
c. green:
d. yellow:
8. Complete the table of probabilities below.
9. Find the probability that the pointer stops in either the blue region or the green region.
10. Find the probability that the pointer does not stop in the green region.

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