Question

Analyze the table below and answer the question that follows.

Plays a Sport
Does Not Play a Sport
Total

Freshman
17
4
21

Sophomore
12
5
17

Junior
9
6
15

Senior
6
8
14

Total
44
23
67

A sample of students were surveyed during lunch and asked whether or not they played a sport. A student randomly chosen from the sample plays a sport. Find the probability that the student is a junior or a senior

Answer 1

The probability that a student randomly chosen from the sample who plays a sport is either a junior or a senior is 15/44, which is approximately 0.3409 or 34.09%.

Step-by-step explanation:

The question asks to find the probability that a student randomly chosen from the sample of students who play a sport is either a junior or a senior. To find this probability, we will look at the table provided and sum up the number of juniors and seniors who play sports and then divide by the total number of students who play sports.

• Number of juniors who play a sport: 9
• Number of seniors who play a sport: 6
• Total number of juniors and seniors who play a sport: 9 + 6 = 15
• Total number of students who play a sport: 44

To calculate the probability, we use the formula:

Probability (junior or senior) = Number of juniors and seniors who play a sport / Total number of students who play a sport

Therefore:

Probability (junior or senior) = 15 / 44

This simplifies to an approximate probability:

Probability (junior or senior) ≈ 0.3409 or 34.09%

Answer 2

P(Junior that plays a sport) = 9/44
P(senior that plays a sport) = 6/44

P(junior or senior that plays a sport) = 9/44 + 6/44 = 15/44