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Problem-Solving and Data Analysis / Probability and conditional probability Difficulty: Hard

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

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

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.)

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Explanation

The correct answer is $StartFraction 23 Over 60 EndFraction$ . 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 $20 plus$ years of age. Therefore, there are $14 plus 9$ , 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 $20 plus$ years of age. Therefore, there are a total of $30 plus 30$ , 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 $StartFraction 23 Over 60 EndFraction$ . Note that 23/60, .3833, and 0.383 are examples of ways to enter a correct answer.