Question

A missile can be accidentally launched if two relays Aand Bboth have failed. The probabilities of Aand 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.
(a) What is the probability of an accidental missile launch?
(b) What is the probability that A will fail if B has failed?
(c) Are the events "A fails" and ''B fails" statistically independent?

Answer 1

Answer:

A. 0.006

B. 0.02

C. They are dependent

Step-by-step explanation:

Given

P(A) = 0.01 ---- The probability that A faile

P(B) = 0.03 --- The probability that B fails

P(B|A) = 0.06 ---- The probability that B will fail if A fails

A. What is the probability of an accidental missile launch?

If an accidental missile is launched, then this means we're asked to calculate the probability that A fails and B fails

This is given by P(A and B)

The expression,

P(B|A)=P(A and B)/P(A) will be used to solve this question.

Substitute in the values

0.06 = P(A and B) / 0.01 ---- Make P(A and B) the subject of formula

P(A and B) = 0.01 * 0.06

P(A and B) = 0.006

B. What is the probability that A will fail if B has failed?

Here, we're to calculate P(A|B)

This is calculated by

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

Where P(A and B) = 0.006

Substitute in the values

P(A|B) = 0.006 / 0.03

P(A|B) = 0.02

C. Are the events "A fails" and ''B fails" statistically independent?

If the occurrence of event A fails does not affect the occurrence of the event B fails and vice versa then they are independent.

Meaning that if P(B|A)=P(B) or P(A|B)=P(A) they are independent.

But P(A|B) = 0.02 and P(A) = 0?01

Since the values are not the same

Then, we can conclude that they are dependent