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emogalaxcy8396
02.03.2020 •
Mathematics
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?
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Ответ:
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
Ответ:
8 and 13 years old respectively.
Step-by-step explanation:
Let r = age of Rachael
Let m = age of Monica
M = r + 5 equation 1
r + m = 21 equation 2
Substituting equation 1 into equation 2;
r + (r +5) = 21
r + r + 5 = 21
Simplifying the equation, we have;
2r + 5 = 21
2r = 21 - 5
2r = 16
r = 16/2 = 8
To find the value of m;
From equation 1;
m = r + 5
Substituting the value of r;
m = 8 + 5
m = 13.
Therefore, Rachael is 8 years old while Monica is 13.