Probability Math Problem

Question

Seniors at a high school took a survey. The results are shown below.

 

                             Drives to School                  Does Not Drive to School                                Row Totals
Favors Rule                     40                                               30                                                        70

 

Opposes Rule                  20                                               10                                                        30

 

Total                                60                                               40                                                       100

 

 

a. How many seniors drive to school?

b. How many seniors favor the rule?

c. How many seniors favor the rule and do not drive to school?

d. What is the probability that a senior chosen at random favors the rule?

e. What is the probability that a senior chosen at random drives to school and favors the rule?

f. What is the probability that a senior chosen at random drives to school or opposes the rule?

g. Are the results of this survey a good indicator of how all of the students at the high school feel about the driving rule? Explain.

Answer 1

(a) Add down the far left column, 40 + 20 = 60 seniors drive to school

(b) Add the top row: 40 + 30 = 70 seniors favor the rule

(c) This is the intersection of the top row and the right column, or 30

(d) The sum of the top row shows that 70 seniors favor the rule. There are a total of 100 seniors. So, the probability that a senior chosen at random favors the rule = 70/100 = 0.7

(e) The number of students who drive to school and favor the rule is the intersection of the left row and top column, or 40. So, the probability that a senior selected at random drives to school and favors the rule is 40/100 = 0.4

(f) To find the number of students who drive to school and oppose the rule, take the intersection of the left column and bottom row, or 20. So, the probability that a senior chosen at random drives to school and opposes the rule is 20/100 = 0.2.

(g) I think so. You see that 70% favor it. You can see this result without having to tabulate whether or not the students drive to school.