Q19. - Algebra 1

Question

EDUCATION Kristin surveys 200 people in her school to determine how many nights a week students do homework. The results are shown.

a. Find the probability that a randomly chosen student will have studied more than 4 nights.

b. Find the probability that a randomly chosen student will have studied no more than 3 nights.

Step-by-Step Solution

Answer

a. The probability that a randomly chosen student will have studied more than four nights is $\frac{1}{20}$.

 

b. The probability that a randomly chosen student will have studied no more than three nights is $\frac{9}{10}$.

Part a Step 1. Probability.

Probability measures likelihood of an event to occur

Part a Step 2. Number of students.

There is total 200 people in the survey. From the given table it can be observed that the number of students will have studied more than 4 nights is 10.

Step 3. Find the probability.

The probability that a randomly chosen student will have studied more than four nights is 

$\begin{array}{l}P=\frac{10}{200}\\ =\frac{1}{20}\end{array}$

Therefore, the probability that a randomly chosen student will have studied more than four nights is $\frac{1}{20}$.

Part b Step 1. Probability.

Probability measures likelihood of an event to occur

Part b Step 2. Number of students.

There is total 200 people in the survey. From the given table it can be observed that the number of students will have studied no more than three nights is 

$90+50+30+10=180$

Part b Step 3. Find the probability.

The probability that a randomly chosen student will have studied no more than three nights is

$\begin{array}{l}P=\frac{180}{200}\\ =\frac{9}{10}\end{array}$

Therefore, the probability that a randomly chosen student will have studied no more than three nights is $\frac{9}{10}$.