Question

The table shows the results of a poll of 200 randomly selected juniors and seniors who were asked if they attended prom. Find the probability of each of the events.

juniors seniors
yes 28 97
no 56 19

Express your answer as a fraction, using the backslash. Example: 17 would be written as 1/7.


a) P (a junior who did not attend prom)

b) P (did not attend prom | senior)

c) P (junior | attended prom)

Answer 1

(a)
`(7)/(25)`

(b)
`(19)/(116)`

(c)
`(28)/(125)`

Explanation:

Number of juniors who attended prom,n(J)=28

Number of seniors who attended prom,n(S)=97

• Total of those who attended prom=125

Number of juniors who did not attend prom,n(J')=56

Number of seniors who did not attend prom,n(S')=19

• Total of those who attended prom=75
• Total Number of students=200

(a) P (a junior who did not attend prom)

`P(J')=(56)/(200)= (7)/(25)`

(b)

`P(Senior)=(116)/(200)`

`P ($did not attend prom$ | senior)=\frac{\text{P(seniors who did not attend prom)}}{P(Senior)} \\=(19/200)/(116/200) \\=(19)/(116)`

(c)P (junior | attended prom)

`P(Senior)=(84)/(200)`

`P (Junior|$ attended prom$)=\frac{\text{P(juniors who attended prom)}}{P(\text{those who attended prom)}} \\=(28/200)/(125/200) \\=(28)/(125)`

Answer 2

A. P = 7/25

B. P = 19/116

C. P = 28/125

Explanation:

1. Let's review the information given to us to answer the question correctly this way:

Juniors Seniors Totals

Yes 28 97 125

No 56 19 75

Totals 84 116 200

2. Find the probability of each of the events.

Let's recall that the formula of probability is:

P = Number of favorable outcomes/Total number of possible outcomes

A. P (a junior who did not attend prom)

P = Juniors who did not attend prom/Total number of students surveyed

P = 56/200

P = 7/25 (Diving by 8 numerator and denominator)

B. P (did not attend prom | senior)

P = Seniors who did not attend prom/Total number of seniors surveyed

P = 19/116

C. P (junior | attended prom)

P = Juniors who attend prom/Total number of students attended prom

P = 28/125