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probability and expectations

The probability in detecting a crack in an airplane wing= probability of inspecting a plane with a wing crack (P1) x probability of inspecting the details in which a crack is located (P2) x probability of detecting the damage (P3)

Find the probability of detecting a crack if (P1=.9, P2=.8 & p3=.5)?
If 50 planes are inspected, what is the probability that at least one wing crack is detected using poisson distribution? if 5 planes inspected find probability Pr(X>=1) based on binomial distribution.

Q2). Administration reported that 185 people died in 12,438 motel and hotel fires. National death rate per 100 persons is worked out; (185/12.438)x100 = 1.5.

In a region where 100 motel/hotel fires occurred, what is the probability that the number of deaths exceeded by 2?

Q3). There are 12 strangers in a lecture hall. What is the probability that the 12 persons celebrate their birthdays in 12 different months?

Q4). Table shows number of strikes S which commenced in a week over the period 1948-1959.

S = 0 , 1 , 2 , 3+
frequency= 252,229, 109, 36

Show that the expected value of S is about 0.95. Take the average value of the (S=3+) as 4.

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solution contains detailed explanation of how to calculate probability