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Problem Solving And Data Analysis · Probability

SAT Probability Practice Questions (Free + Explanations) | Quiz 7

Question 12345 of 5

Question 1 of 5

A wildlife center is tagging birds before releasing them. Of the 120 birds tagged, 45 are hawks and the rest are owls. One bird is selected at random from the tagged birds, and then a second bird is selected at random without replacement. What is the probability that both selected birds are hawks?

Explanation

There are 120 tagged birds total, and 45 of them are hawks. The probability that the first bird selected is a hawk is . Because the first bird is not replaced, there are now 119 birds left, and 44 of them are hawks. So the probability that the second bird is also a hawk is . Multiply the probabilities:

Therefore, the probability that both selected birds are hawks is .

Concept summary

For two selections without replacement, multiply the probability of the first event by the probability of the second event after the total number of items has changed.

Question 2 of 5

A bag contains 5 red marbles and 7 blue marbles. Two marbles are drawn at random without replacement. Which expression is equivalent to the probability that the two marbles are different colors?

Explanation

To get two marbles of different colors, there are two possible orders: red then blue, or blue then red.

The probability of drawing a red marble first and then a blue marble is

The probability of drawing a blue marble first and then a red marble is

These two probabilities are equal, so the total probability is

Therefore, the equivalent expression is .

Concept summary

For probability without replacement, multiply probabilities along each valid sequence, then add the sequences that satisfy the condition.

Question 3 of 5

A weather station plots each day's forecast and outcome on a coordinate grid. For each of 100 days, the -coordinate is the predicted chance of rain (in percent), and the -coordinate is 1 if it rained that day and 0 if it did not. Among the 40 plotted points with -values from 60 through 79, exactly 28 have . Based on these data, which value is closest to the experimental probability that it rained on a day when the predicted chance of rain was from 60% through 79%?

Explanation

The question asks for the experimental probability that it rained, given that the predicted chance of rain was from 60% through 79%. That means we look only at the 40 days in that -value range. Of those 40 days, 28 have , meaning it actually rained. So the experimental probability is . Therefore, the value closest to the experimental probability is .

Concept summary

Experimental probability is found by dividing the number of times the event occurred by the total number of relevant trials. On a graph, this often means counting only the points that meet a given condition.

Question 4 of 5

A jar contains 4 red marbles, 3 blue marbles, and 2 green marbles. Two marbles are drawn at random without replacement. Which of the following must be true about the probability that the two marbles are different colors?

Explanation

To find the probability that the two marbles are different colors, it is often easier to first find the probability that they are the same color and subtract from 1.

There are 9 marbles total, so the total number of ways to draw 2 marbles is

Now count the same-color pairs:
- Red-red:

- Blue-blue:

- Green-green:

So the number of same-color pairs is

Thus, the probability of drawing 2 marbles of the same color is

Therefore, the probability of drawing 2 marbles of different colors is

Since

the statement that must be true is that the probability is greater than .

Concept summary

For probability questions involving two draws without replacement, counting combinations is often efficient. A useful strategy is to find the complement first when it is easier to count.

Question 5 of 5

A circular garden has radius 10 feet. A sprinkler is set to water a sector of the garden with a central angle of . If a point is chosen at random from the garden, what is the probability that the point lies in the watered sector?

Explanation

The probability is the fraction of the garden's area that is watered. Since the watered region is a sector of the circle, its area is proportional to its central angle. So the probability is . Therefore, the correct answer is .

Concept summary

For a point chosen uniformly at random from a circle, the probability of landing in a sector equals the sector's area divided by the circle's total area. Because sector area is proportional to central angle, this probability is .

Your results

0of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

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Your results

1of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

2of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

3of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

4of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

5of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice