Question

A door alarm works in 72 out of 100 cases and surveillance camera works in 68 out of 100 cases. What is the probability of effective screening techniques keeping in mind that these two methods can be used together

Answer 1

The door alarm works in 72 out of 100 cases. And the surveillance camera works in 68 of 100 cases.


Let us assume two events:

Event A = Door Alarm Works
Event B = Surveillance Camera Works



Then we can get the Probability of the two events:

$P(A) = \frac{72}{100} = 0.72 \\ \\ P(B) = \frac{68}{100} = 0.68$


Now, we have to find the probability that our screening technique would work together. That is, we have to find the probability that both the door alarm and surveillance camera would work in a specific case.


In mathematical terms, we have to find $P(A \cap B)$

Both A and B are independent events. Because, the happening of Event A is not related to B. And similarly, the happening of Event B is not related to Event A.

The door alarm and surveillance camera work independently.


So, we can write:

$P(A\cap B) = P(A) . P(B) \\ \\ \implies P(A \cap B) = 0.72 \times 0.68 \\ \\ \implies \boxed{\bold{P(A\cap B) = 0.4896}}$

Thus, The Probability that both screening methods can be used together is 0.4896

Answer 2

Find the probability that the door alarm works:

Number of door alarm cases = 100

Number of time alarm works = 72

P(alarm works) = 72/100 = 18/25

Find the probability that the surveillance camera works:

Number of surveillance camera cases = 100

Number of time surveillance camera works = 68

P( surveillance camera works) = 68/100 = 17/25

Find the probability of both working:

P(both working at the same event) = (18/25) (17/25) = 305/625

Answer: The probability is 305/625