IXL - Find probabilities using combinations and permutations (Geometry practice)

Nicole was on the internet researching prices of new and used cars. One website had 8 cars for sale, 6 of which were station wagons.

If Nicole randomly chose to look at 4 of the cars on the website, what is the probability that all of them are station wagons?

Write your answer as a decimal rounded to four decimal places.

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Learn with an example

question

Levi conducted an experiment to see which one of his friends has the best sense of smell. He bought 8 scratch-and-sniff stickers, 6 of which smelled like cinnamon.

If after his first day of smell-tests, Levi's friends had randomly scratched and sniffed 5 stickers, what is the probability that all of them smelled like cinnamon?

Write your answer as a decimal rounded to four decimal places.

key idea

A uniform probability model is a sample space in which all outcomes are equally likely.

In a uniform probability model, the probability of an event

is the number of outcomes in that event divided by the total number of outcomes in the sample space:

(

)

# of outcomes in

total # of outcomes

A factorial is a whole number followed by an exclamation point. The value of

is 1, and for a positive integer

(

–

)

The number of ways to choose

different objects from a set of

objects is

(

–

)

solution

To find the probability that all 5 stickers smelled like cinnamon, first identify the sample space and the event.

The sample space consists of outcomes that are ways to choose 5 stickers from the set of 8 stickers. In other words, each outcome is a subset of 5 stickers. Each subset is equally likely, so this is a uniform probability model.

The event is that all 5 stickers smelled like cinnamon.

Since this is a uniform probability model, count the number of outcomes in the event and count the total number of outcomes, then divide them to compute the probability.

Count the total number of outcomes.

Each outcome in the sample space is a subset of 5 stickers chosen from the set of 8 stickers. So, the total number of outcomes is the number of ways to choose 5 stickers from the set of 8, which is

total # of outcomes

Count the number of outcomes in the event.

Count the number of outcomes in which all 5 stickers smelled like cinnamon. There are

ways to choose 5 stickers from the set of 6 stickers that smelled like cinnamon.

# of outcomes in the event

Find the probability.

The probability that all 5 stickers smelled like cinnamon is

≈

0.1071

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Teacher tools

Work it out

Not feeling ready yet? These can help:

AA.7Permutation and combination notation

JJ.1Probability of simple events

AA.4Probability of independent and dependent events

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