In his Final exam a Professor permits the use of PCs on the

In his Final exam, a Professor permits the use of PCs on the condition that Wi-Fi is turned off. He has known that 1 out of 15 students will disobey his rule, therefore he does a random check. Find the probability that the first student to disobey (turned on Wi-Fi) was found after 10 students were checked. 0.46 0.48 0.50 0.54

Solution

8.

For a geometric distribution, the probability of first success in 10 trials is

P(X >= x) = (1-p)^(x-1)

As x = 10, p = 1/15,

P(X >= 10) = (1-1/15)^(10-1) = 0.537441241 = 0.54 [ANSWER, D]