SAT question 6a715bed (Probability And Conditional Probability)

Question

The table summarizes the distribution of age and assigned group for $90$ participants in a study.

	$0$ – $9$ years	$10$ – $19$ years	$20$ + years	Total
Group A	$7$	$14$	$9$	$30$
Group B	$6$	$4$	$20$	$30$
Group C	$17$	$12$	$1$	$30$
Total	$30$	$30$	$30$	$90$

One of these participants will be selected at random. What is the probability of selecting a participant from group A, given that the participant is at least $10$ years of age? (Express your answer as a decimal or fraction, not as a percent.)

College Board · Accepted Answer

The correct answer is 23/60,.3833,0.383. The correct answer is (23)/(60) . It's given that one of the participants will be selected at random. The probability of selecting a participant from group A given that the participant is at least 10 years of age is the number of participants in group A who are at least 10 years of age divided by the total number of participants who are at least 10 years of age. The table shows that in group A, there are 14 participants who are 10 – 19 years of age and 9 participants who are 20 + years of age. Therefore, there are 14 + 9 , or 23 , participants in group A who are at least 10 years of age. The table also shows that there are a total of 30 participants who are 10 – 19 years of age and 30 participants who are 20 + years of age. Therefore, there are a total of 30 + 30 , or 60 , participants who are at least 10 years of age. It follows that the probability of selecting a participant from group A given that the participant is at least 10 years of age is (23)/(60) . Note that 23/60, .3833, and 0.383 are examples of ways to enter a correct answer.

CookSAT · Answer

Note: The 'given at least 10 years' condition restricts the sample space to the last two age columns, so the denominator is 30+30=60, not 90.

Explanation

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SAT Question 6a715bed: Probability And Conditional Probability answer and explanation with Desmos solution

Explanation

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