Question

Using the demographic information in the table below, consider the following scenario: A teacher chooses a student to dim the lights and a student to shut the door. If a student may do both jobs, determine the following probabilities.

Total number of students in the class	50
Number of Boys	35
Number of girls	15
Number of freshman	22
Number of sophomores	13
Number of juniors	9
Number of seniors	6
Number of education majors	7
Number of non-education majors	43

a. P(Both are girls)

b. P(one is a girl and one is a boy)

c. P(at least one is a boy)

       i. Find the probability using cases

      ii. Next, calculate the probability using the complement rule.

d. P (The door closer is a boy)

e. P(neither are seniors)

e. Neither are seniors?

f. Neither are education majors?

Answer 1

Answer:

Given data,

Using the demographic information in the table below, consider the following scenario: A teacher chooses a student to dim the lights and a student to shut the door. If a student may do both jobs, determine the following probabilities.

Total number of students in the class	50
Number of Boys	35
Number of girls	15
Number of freshman	22
Number of sophomores	13
Number of juniors	9
Number of seniors	6
Number of education majors	7
Number of non-education majors	43

(a).

Probability that both are girls is computed here as:

= (15/50)² = 0.09

Therefore 0.09 is the required probability here.

(b).

Probability that one is girl and the other is boy:

= Probability to select a girl Probability to select a boy + Probability to select a boy Probability to select a girl

= (15/50)(35/50) + (35/50)(15/50)

= 0.42

Therefore 0.42 is the required probability here.

(c) .

Probability that there is at least one boy selected:

= 1 - Probability that both were girls selected.

= 1 - 0.09

= 0.91

Therefore 0.91 is the required probability here.

(d).

Probability that the door closer is a boy:

= Number of boys / Total number of students

= 35/50

= 0.7

Therefore 0.7 is the required probability here.

(e).

Probability that neither are seniors:

= [(Total number of students - Total number of seniors ) / Total number of students ]²

= [(50 - 6)/50 ]²

= 0.7744

Therefore 0.7744 is the required probability here.

(f)

Probability that neither are education majors:

= [(Total number of students - Total number of education majors ) / Total number of students ]²

= [(50 - 7)/50 ]²

= 0.7396

Therefore 0.7396 is the required probability here.