Answer:
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
