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
