Section A Section A Checkpoint

Problem 1

A kindergarten teacher has a set of 20 cards to help students learn to count. Each card has a number of animals on it, from 1 to 20.

One child can count to 15 well, but has problems with 16 and after. When this child picks a card at random, what is the probability that it will be a number they have problems with?

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Solution

\frac{5}{20}, \frac{1}{4}, 25\%

(or equivalent)

Show Sample Response

Sample Response

\frac{5}{20}, \frac{1}{4}, 25\%

(or equivalent)

Problem 2

An environmental scientist can determine the health of a river based on whether a particular insect is present when they collect a sample of water. The scientist and students collect 25 samples from different parts of a river and notice that the insect is present in 12 of them.

The river is considered healthy if the probability of finding the insect in a sample is $\frac{1}{2}$ . Do you think this river could be considered healthy? Explain your reasoning.
What could the scientist do to better estimate the probability of finding the insect in a sample of river water?

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Solution

Sample response:

I think it might be considered healthy. Sample reasoning: With a probability of $\frac{1}{2}$ , we might expect that 12.5 of the 25 samples have the insect. Because 12 samples had the insect, and that is pretty close to the expected 12.5, it might be close to a probability of $\frac{1}{2}$ .
The scientist could collect more samples.

Show Sample Response

Sample Response

Sample response:

I think it might be considered healthy. Sample reasoning: With a probability of $\frac{1}{2}$ , we might expect that 12.5 of the 25 samples have the insect. Because 12 samples had the insect, and that is pretty close to the expected 12.5, it might be close to a probability of $\frac{1}{2}$ .
The scientist could collect more samples.