Question

A missile can be accidentally launched if two relays A and B both
have failed. The probabilities of A and B failing are known to be 0.01
and 0.03 respectively. It is also known that B is more likely to fail
(probability 0.06) if A has failed.
(i) What is the probability of an accidental missile launch?
(ii) What is the probability that A will fail if B has failed?
(iii) Are the events “A fails” and “B fails” statistically
independent

Answer 1

Answer:

robability B fails given A fails, P(B|A), is given as .06

P(A)=.01

P(B)=.03

part a would be the probability A and B fail, P(A and B)

P(B|A)=P(A and B)/P(A)

 

.06=P(A and B)/.01

P(A and B)=.0006

part b, P(A|B)=P(A and B)/P(B)

We now have P(A and B)=.0006 from part a. Use this to answer part b.

P(A|B)=.0006/.03=.02

part c, the events are independent if the occurence of one does not affect the occurence of the other. That is, if P(B|A)=P(B) or P(A|B)=P(A) they are independent.

Are they the same?.

Step-by-step explanation: