A statistics professor classifies his students according to their grade point av

Question

A statistics professor classifies his students according to their grade point average (GPA) and their gender. The accompanying table gives the proportion of students falling into the various categories. One student is selected at random. Under 2.0 2.0-3.0 Over 3.0 Total Male (M) Female (F) Totals 05 10 15 25 30 10 20 .30 40 60 1.00 (a) If the student selected is female, what is the probability that her GPA is between 2.0 and 3.0? (b) If the GPA of the student selected is over 3.0, what is the probability that the student is male? (c) What is the probability that the student selected is female or has a GPA under 2.0 on both? (d) Is GPA over 3.0 independent of gender? Explain using probabilities

Explanation / Answer

Ans:

a)

P(2.0-3.0/female)=P(female and 2.0-3.0)/P(female)

=0.30/0.60

=0.5

b)P(male/over 3.0)=P(male and over 3.0)/P(over 3.0)

=0.10/0.30

=1/3=0.33

c)P(female or under 2.0)=P(female)+P(under 2.0)-P(female and under 2.0)

=0.60+0.15-0.10

=0.65

d)P(Over 3.0 and female)=0.20

P(over 3.0)=0.30

P(female)=0.60

P(over 3.0)*P(female)=0.30*0.60=0.18

As,P(Over 3.0 and female) is not equal to P(over 3.0)*P(female),so not independent.

  

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