There are 1000 students in a high school Among the 1000 stud

There are 1000 students in a high school. Among the 1000 students, 800 students have a laptop, and 300 students have a tablet. 150 students have both devices. 11. What is the probability that a randomly selected student has neither device? (10 pts) 12. What is the probability that a randomly selected student has a laptop, given that he/she has a tablet? (5 pts) 13. Let event A be the selected student having a laptop, and event B be the selected student having a tablet. Are A and B independent events? Why or why not? (5 pts)

Solution

P( student have Laptop) = 800/1000 = 0.8

P(student have tablet ) = 300/1000 = 0.3

P( Student have Laptop and tablet) = 150/1000 = 0.15

P( Student either has Laptop or Tablet) = 0.8 + 0.3 - 0.15 = 0.95

11.

P( Students has neither device) = 1 - P( Student either has Laptop or Tablet) = 1 - 0.95 = 0.50

12.

P( Student has Laptop given that he has tablet = P( Student have Laptop and tablet) / P( Student has Tablet) = 0.15/0.3 = 0.5

13.

P(A) = 0.8 ; P(B) = 0.3 P(A and B) = 0.15

P(A) * P(B) = 0.8*0.3 = 0.24

P(A n B) != P(A) * P(B) by this A, B are not independent events