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. 250 students have both devices.

What is the probability that a randomly selected student has neither device?

What is the probability that a randomly selected student has a laptop, given that he/she has a tablet?

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?

Solution

P(A) = 800/1000 = 0.80

P(B) = 300/1000 = 0.30

P(A and B) = 250/1000 = 0.25

probability that a randomly selected student has neither device = 1 - P(A or B) = 1 - [P(A) + P(B) - P(A and B)]

= 1 - [0.8 + 0.3 - 0.25] = 0.15

probability that a randomly selected student has a laptop, given that he/she has a tablet = P(A | B)

= P(A and B) / P(B)

=0.25 / 0.30 = 0.8333

P(A)*P(B) = 0.8*0.3 = 0.24 which is not equal to P(A and B)

So, A and B are not independent as they do not satisfy: P(A and B) = P(A)*P(B)