A survey of 140 students in the 9th and 10th grades asked about their preferred after-scho… — SAT

A survey of 140 students in the 9th and 10th grades asked about their preferred after-school activity. The results are summarized in the table below.

Grade	Sports	Arts	Total
9th Grade	40	20	60
10th Grade	30	50	80
Total	70	70	140

If a student is selected at random from the 9th-grade students, what is the probability that the selected student preferred sports?

A
$\frac{2}{7}$
B
$\frac{1}{3}$
$\frac{2}{3}$ Answer
D
$\frac{4}{7}$

Answer

\frac{2}{3}

The correct answer is

\frac{2}{3}

. The question asks for the probability that a student preferred sports, given that the student is in the 9th grade. This means we only consider the 60 students in the 9th grade. Of those 60 students, 40 preferred sports. Therefore, the probability is

\frac{40}{60}

, which simplifies to

\frac{2}{3}

Step-by-Step Solution

Identify the group of interest from which the student is selected.

The selection is made from the 9th-grade students, so the denominator for the probability is the total number of 9th-grade students, which is

60

The problem states: 'If a student is selected at random from the 9th-grade students,' establishing this as a conditional probability where the sample space is restricted to 9th graders.

Identify the number of students within this group who satisfy the target condition.

The number of 9th-grade students who preferred sports is

40

We look at the intersection of the '9th Grade' row and the 'Sports' column in the table.

Calculate the probability by dividing the number of target outcomes by the total outcomes in the conditional sample space, and simplify the fraction.

The probability is

\frac{40}{60}

, which simplifies to

\frac{2}{3}

Dividing both the numerator and the denominator by their greatest common divisor, 20, gives the simplified probability.

Key Concept

Calculating conditional probability from a two-way frequency table by restricting the sample space to a specific row or column.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic