Question

Consider 100 planes sent out and only 50 came back, 30 with fuselage and 20 with engine damaged, 10 undamaged. The rest are shot down due to either of the damage, or both. Further assume that the probabilities of fuselage and engine damages are 0.7 and 0.4, respectively. What is the chance of survival under both damages? (8pt) Are engine and fuselage damage events independent? (2pt)

Answer 1

1.> What is the chance of survival under both damage? Ans: 0.5 chances of survival under both damage

chance of survival under fuselage damage is 3/7=0.42857 and  chance of survival under engine damage is 0.5.

both this events are not indepandent hance chances of survival under both damage is 0.5

2.> Are engine and fuselage damage evenets independent? Ans : No its not independent

two random variables are independent if the realization of one does not affect the probability distribution of the other,

i.e., for variables A and B, if and only if P(A|B) = P(A) and P(B|A) = P(B), A and B are independent.