4 Your friend will come to visit you. Suppose that he will come by train with probability 1/6; by ship, car, or plane with probabilities 1/6, 1/6, or 1/2, respectively. If the probability is that he will be late by train; 1/3, 1/12 by ship, car, respectively; 0 by plane. Find the probability that your friend will be late.

0.1515

0.2222

0.1111

0.2020

5 Refer to question 4. Suppose we knew that he was late for the visit. What is the probability that he came by train?

0.3507

0.3750

0.3570

0.3057

6 Refer to question 4. Suppose we knew that he was not late for the visit. What is the probability that he came by train?

Group of answer choices

0.6250

0.1406

0.1640

0.4016

7 A bin contains 3 different types of disposable flashlights. The probability that a type 1 flashlight will give over 100 hours of use is 0.8, with the corresponding probabilities for type 2 and type 3 flashlights being 0.6 and 0.5, respectively. Suppose that 50 percent of the flashlight in the bin are type 1, 30 percent are type 2, and 20 percent are type 3. What is the probability that a randomly chosen flashlight will give more than 100 hours of use?

Group of answer choices

0.70

0.66

0.68

0.78

9 Refer to question 7. Given that a flashlight didn't last over 100 hours, what is the conditional probability that it was not type 1 flashlight?

Group of answer choices

0.6587

0.6578

0.6785

0.6875