Question

Conditional Probability

Problem 1 Conditional probability

In group of 200 university students, 140 are full time students (80 females and 60 males) and 60 no full time students (40 females and 20 males).

Let

   M=event a student is male

   W=event a student is a female

   F=event a student is full time

   F^C= event a student is not full time

1) Find the probability that a student is male and full time   

2) Find the probability that a student is male and is not full time   

3) Find the probability that a student is female and full time

4) Find the probability that a student is female and not full time   

5) Find complete the following   

Table1.1: Joint probability table for full time student

	Full time	Not full time	Total
Male
Female
Total

6) Find the conditional probabilities   

      6.1)the probabilities of full time for a male student   

      6.2) the probabilities of full time for a female student

Answer 1

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1) Find the probability that a student is male and full time

P(student is male and is full time) = 60/200 = .30

2) Find the probability that a student is male and is not full time

P(student is male and is not full time) = 20/200 = .10

3) Find the probability that a student is female and full time

P(student is female and full time) = 80/200 = .40

4) Find the probability that a student is female and not full time

P(female and not full time) = 40/200 = .20

5) Find complete the following

6) Find the conditional probabilities

6.1)the probabilities of full time for a male student

P(given male, he' full time) = P(make full time)/P(male) = 60/(60+20) = .75

6.2) the probabilities of full time for a female student

P(given female , she' full time) = P(female full time)/P(female) = 80/(80+40) = .67