Question

Joel surveyed his class asking the question “Do you like school?” The results are as follows:

Liked Disliked No opinion Total

Male 12 5 2

Female 10 3 1

Total

Suppose you draw randomly from the students who answered this survey:

a) given that the student is male, what is the probability that the student likes school?

b) what is the probability of selecting a female given that dislikes school?

c) find the probability that the student is a male or dislikes school.

d) find the probability that the student is female and has no opinion.

e) if the two different (without replacement) students are selected, find the probability that both disliked schools.

Answer 1

a) Given that the student is male, the probability that the student likes school

$= \frac{12}{12 + 5 +2}$

$= \frac{12}{19}$

$= 0.6316$

b) The probability of selecting a female given that dislikes school

$= \frac{3}{5+3}$

$= \frac{3}{8}$

$= 0.375$

c) Total number of students = 12 + 5 + 2 + 10 + 3 + 1 = 33

The probability that the student is a male or dislikes school

= P(student is male) + P(the student dislikes school) - P(student is male and dislikes school)

$= \frac{12+5+2}{33} + \frac{5+3}{33} - \frac{5}{33}$

$= \frac{19}{33} + \frac{8}{33} - \frac{5}{33}$

$= \frac{19+8-5}{33}$

$= \frac{22}{33}$

$= 0.66667$

d) The probability that the student is female and has no opinion

$= \frac{1}{33}$

$= 0.030303$

e) Number of students who dislike the school = 5 + 3 = 8

If the two different (without replacement) students are selected, the probability that both disliked schools

$= \frac{8*7}{33*32}$

$= 0.053$