SAT Probability and conditional probability Question

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Question 1 · Hard · MathNovember 2024 Batch 4 · Q18Probability and conditional probability · 0 solved

Classification	Less than 20	20 to 30	Greater than 30
Sensory neuron	13	7	3
Motor neuron	0	15	18
Interneuron	10	34	0

For 100 neurons, the table summarizes the distribution of classification and cell body diameter. One of these neurons will be selected at random. What is the probability of selecting a neuron with a cell body diameter that is less than or equal to 30 micrometers, given that it is not classified as a motor neuron? (Express your answer as a decimal or fraction, not as a percent.)

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Strategy

For conditional probability, first restrict the sample space to the condition after the word “given.” Then count how many of those outcomes also satisfy the event, and form a fraction. A table question like this usually requires combining multiple cells, so make sure you include every category that fits both conditions and exclude every category that does not.

Hints (open one at a time)

Hint 1

Focus on the group after the word “given”: that is the only group that matters in the denominator.

Hint 2

Add the counts from the categories that are not motor neurons to get the total group size, then add the counts with diameter at most 30 to get the favorable count.

Hint 3

Use the cells for sensory neurons and interneurons only, and include both diameter columns up to 30 before writing the fraction.

Step-by-step Explanation

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