Chapter 5.2, Problem 44E

(a)

To determine

Probability that the student is a sixth − grader or rated good grades as important.

Answer to Problem 44E

Probability,

  $P\left(6^{\text{th}}\text{grade}\text{or}\text{Grades}\right)\approx 0.6985$

Explanation of Solution

Given information:

Survey data:

  

Look at the bottom right corner of the table,

There are 335 students in total.

Thus,

The number of possible outcomes is 335.

Also,

For the student who are rated good grades or 6^th grader,

Add up all the values in column “Grades” and row “6th grade”, we will get 234 in total.

Thus,

The number of favorable outcomes is 234.

Now,

The number of favorable outcomes divided by the number of possible outcomes gives the probability.

  $\begin{array}{l}P\left(6^{\text{th}}\text{grade}\text{or}\text{Grades}\right)=\frac{\text{Number}\text{of}\text{favourable}\text{outcomes}}{\text{Number}\text{of}\text{possible}\text{outcomes}}\\ =\frac{234}{335}\\ \approx 0.6985\end{array}$

(b)

To determine

Probability that the student is not a sixth − grader and did no rate good grades as important.

Answer to Problem 44E

Probability,

  $P\left(\text{Not}{6}^{\text{th}}\text{grader}\text{and}\text{no}\text{Grades}\right)\approx 0.3015$

Explanation of Solution

Given information:

Survey data:

  

Look at the bottom right corner of the table,

There are 335 students in total.

Thus,

The number of possible outcomes is 335.

Also,

For the student who did not rate good grades and not a 6^th grader as well,

Add up all the values of 4^th and 5^th grades in the columns “Athletic” and “Popular”, we will get 101 in total.

Thus,

The number of favorable outcomes is 101.

Now,

The number of favorable outcomes divided by the number of possible outcomes gives the probability.

  $\begin{array}{l}P\left(\text{Not}{6}^{\text{th}}\text{grader}\text{and}\text{no}\text{Grades}\right)=\frac{\text{Number}\text{of}\text{favourable}\text{outcomes}}{\text{Number}\text{of}\text{possible}\text{outcomes}}\\ =\frac{101}{335}\\ \approx 0.3015\end{array}$