135 UB students were surveyed and asked how many hours a week they spent studying. The results are in the table below?
135 UB students were surveyed and asked how many hours a week they spent studying. The results are in the table below?
Less than 5hrs (5 to10hrs) (More than 10) Total

Male (M) 25 25 20 70

Fmale (F) 20 30 15 65

Total 45 55 35 135

a) Complete the joint and marginal probability.

b) Find the probability that a student studied 5 to 10 hours.

c) Find the probability that a student is a male and spends less than 5 hours studying.

d) Find the probability that a student is a female or spends more than 10 hours studying.

e) Find the probability that a student spends more than 10 hours studying given that the student is a female?

f) Find the probability that a student is a male given that he spends less than 5 hours studyin

B) 11/27 ; c.) 5/27; D.) 17/27; E.) 3/13 ; F) 5/9

Step-by-step explanation:

- - - - - <5hrs - - (5 - 10hrs) - - (>10 hrs) - - Total

Male (M) 25 - - - - -- 25 - - - - - 20 - - - - 70

Female (F) 20 - - - - - - 30 - - - - - 15 - - - - 65

Total - - - 45 - - - - - - 55 - - - - - 35 - - - - 135

Probability = (required outcome / Total possible outcomes)

B) probability that a student studied(5 - 10 hours)

P(5 to 10 hours) = n(5 - 10 hours) / n(total) = 55/135 = 11/27

C) Find the probability that a student is a male and spends less than 5 hours studying

P(male and < 5 hours) = n(male ∩> 5 hours) / n(total) = 25/135 = 5/27

D) Find the probability that a student is a female or spends more than 10 hours studying.

P(female) + P(> 10hours) - P(Female ∩ > 10 hours) = 65/135 + 35/135 - 15/135 = 85/135 = 17/27

E.) Find the probability that a student spends more than 10 hours studying given that the student is a female?

n(Female ∩ > 10 hours) / n(Female)

15/65 = 3/13

F) Find the probability that a student is a male given that he spends less than 5 hours studying

n(male ∩ < 5hrs) / n(< 5 hours) = 25/ 45 = 5/9

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