Free Practice Question

PS · Problem Solving

655-705

Probability

There are three boys aged 3, 5, and 8, and three girls aged 4, 7, and 10. If two boys and two girls are chosen at random, and the sum of their ages is denoted by $z$ , what is the difference between the probability that $z$ is even and the probability that $z$ is odd?

Answer Choices

Correct answer marked below

A

\frac{1}{2}

B

\frac{1}{3}

C

\frac{2}{3}

D

\frac{1}{4}

\frac{1}{9}

Correct

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Explanation

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Official Explanation

Official

To solve the problem, we need to determine the difference between the probability that the sum of the ages of two chosen boys and two chosen girls is even and the probability that it is odd. Let's break down the solution step by step.

Step 1: List the Ages

- Boys' Ages: 3, 5, 8

- Girls' Ages: 4, 7, 10

Step 2: Calculate the Sum of Ages for Boys and Girls

First, we calculate the sum of ages when two boys are chosen and when two girls are chosen.

- Sum of Boys' Ages Taken Two at a Time:

- 3 + 5 = 8

- 3 + 8 = 11

- 5 + 8 = 13

- Sum of Girls' Ages Taken Two at a Time:

- 4 + 7 = 11

- 4 + 10 = 14

- 7 + 10 = 17

Step 3: Determine All Possible Combinations

Next, we consider all possible combinations of the sums of the boys' ages and the sums of the girls' ages. Each combination will give us a possible value of

z

, which is the total sum of the ages of two boys and two girls.

- Possible Combinations:

- 8 (boys) + 11 (girls) = 19

- 8 (boys) + 14 (girls) = 22

- 8 (boys) + 17 (girls) = 25

- 11 (boys) + 11 (girls) = 22

- 11 (boys) + 14 (girls) = 25

- 11 (boys) + 17 (girls) = 28…

There are three boys aged 3, 5, and 8, and three girls aged 4, 7, and 10. If two boys and two girls are chosen at random, and the sum of their ages is denoted by $z$ , what is the difference between the probability that $z$ is even and the probability that $z$ is odd?

Answer Choices

See the full step-by-step explanation

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Official Explanation

Step 1: List the Ages

Step 2: Calculate the Sum of Ages for Boys and Girls

Step 3: Determine All Possible Combinations

Read the full explanation

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What it tests

Common trap

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There are three boys aged 3, 5, and 8, and three girls aged 4, 7, and 10. If two boys and two girls are chosen at random, and the sum of their ages is denoted by zzz, what is the difference between the probability that zzz is even and the probability that zzz is odd?

Answer Choices

See the full step-by-step explanation

Track your performance and improve

Official Explanation

Step 1: List the Ages

Step 2: Calculate the Sum of Ages for Boys and Girls

Step 3: Determine All Possible Combinations

Read the full explanation

No comments yet

What it tests

Common trap

Unlock full explanations

There are three boys aged 3, 5, and 8, and three girls aged 4, 7, and 10. If two boys and two girls are chosen at random, and the sum of their ages is denoted by $z$ , what is the difference between the probability that $z$ is even and the probability that $z$ is odd?