The TV Show MythBusters puts a popular myth to the test on e

The TV Show “MythBusters” puts a popular myth to the test on each episode. The myth is either verified as true or disproven as false (that is, “busted”). Of the myths put to the test on the show, 60% get busted. Many of the myths involve fire, and of these, 80% get busted. Of all the other myths that don’t involve fire, 50% get busted. Show Work.

(a) If a myth involves fire, what is the chance that it will be verified as true?

(b) You watch an episode of MythBusters. What is the chance that it involves fire?

(c) Suppose that on the next episode of MythBusters the myth is verified as true. What is the chance that it involved fire

Solution

Given that,Pr[myth busted] = 0.6

Pr[myth is true] = 0.4

Pr [ myth involves fire get busted] = 0.8

Pr [ myth with out fire fire get busted] = 0.5

a) Pr [ myth involves fire is true ] = 0.4*0.2 =0.08

b) Pr [ that an episode involves fire ] = 0.6*0.8+0.4*0.2 = 0.48 + 0.08 = 0.56

c) Pr [ involving fire / it is true ] = Pr [ myth involves fire is true ] / Pr[myth is true] = 0.08/0.4=0.2