Three radar sets, operating independently, are searching for “hook” echoes (a radar signature associated with tornados). Suppose that each radar has a probability of 0.05 of failing to detect this...

Three radar sets, operating independently, are searching for “hook” echoes (a radar signature associated with tornados). Suppose that each radar has a probability of 0.05 of failing to detect this signature when a tornado is present.

a. Sketch a Venn diagram for a sample space appropriate to this problem.

b. What is the probability that a tornado will escape detection by all three radars?

c. What is the probability that a tornado will be detected by all three radars?