Question

One organization argues that the sonar system using in the Navy constitutes a substantial risk to marine life, such as causing extraordinary numbers of stranded or beached whales. There are the following statements. a. On any given day, the probability of a mass stranding of whales in this area is 0.01. b. The probability of a military exercise on any given day is 0.001. c. If there is a military exercise, the probability of a mass stranding is 0.17.

1. (3pts) Define events and write a probability statement for each fact above.

2. (3pts) On a randomly selected day, what is the probability of a mass stranding of whales and a military exercise.

3. (4pts) Are the events mass stranding and military exercise independent? Justify your answer.

Answer 1

a)

event are

A = mass stranding of whales in this area

and

B= a military exercise on any given day ,

the probability of a mass stranding of whales in this area ,P(A) =  0.01

The probability of a military exercise on any given day , P(B) =  0.001

P(A|B) = 0.17

b) the probability of a mass stranding of whales and a military exercise = P(A and B) = P(A|B)*P(B) = 0.17 * 0.001 = 0.00017

c) since, P(A|B) ╪ P(A) , so events are not independent.