Chapter 5: Q. 44 (page 327)

Middle school values Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked whether good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data.
Suppose we select one of these students at random. What’s the probability of each of the following?
a. The student is a sixth-grader or rated good grades as important.
b. The student is not a sixth-grader and did not rate good grades as important.

Short Answer

Expert verified

a. The probability that the student is a sixth − grader or rated good grades as important is $0.6985$

b. The probability that the student is not a sixth − grader and did no rate good grades as important is $0.3015$

Step by step solution

Part (a) Step 1 : Given Information

We have to determine the probability that the student is a sixth − grader or rated good grades as important.

Part (a) Step 2 : Simplification

Take a look at the table's bottom right corner.

In total,

335

students are enrolled.

Thus,
There are

335

different outcomes to choose from.

Also,

For students who have received good grades or are in the sixth grade,

We'll obtain

234

total if we add all the values in column "Grades" and row "

6 t h

grade."

Thus,

There are a total of

234

positive outcomes.

Now,

The probability is calculated by dividing the number of favourable outcomes by the total number of possible possibilities.

$P (6 t h g r a d e o r G r a d e s) = \frac{N u m b e r o f f a v o u r a b l e o u t c o m e s}{N u m b e r o f p o s s i b l e o u t c o m e s} = \frac{234}{335} \approx 0.6985$

Part (b) Step 1 : Given Information

We have to determine the probability that the student is not a sixth − grader and did no rate good grades as important.

Part (b) Step 2 : Simplification

Take a look at the table's bottom right corner.

In total,

335

students are enrolled.

Thus,

There are

335

different outcomes to choose from.

Also,

For the pupil who did not have good grades and was not in sixth grade,

We'll get

101

if we add all the values from the

4 t h

and

5 t h

grades in the columns "Athletic" and "Popular."

Thus,

The total number of positive outcomes is

101

Now,

The probability is calculated by dividing the number of favourable outcomes by the total number of possible possibilities.

$P (N o t 6 t h g r a d e r a n d n o G r a d e s) = \frac{N u m b e r o f f a v o u r a b l e o u t c o m e s}{N u m b e r o f p o s s i b l e o u t c o m e s} = \frac{101}{335} \approx 0.3015$