In a batch of 10 laser diodes, two have low efficiency, six have moderate effici
ID: 3181841 • Letter: I
Question
In a batch of 10 laser diodes, two have low efficiency, six have moderate efficiency, and two have high efficiency. Two diodes are selected at random without replacement. Let A denote the event that the first diode selected has low efficiency and let B denote the event that the second diode selected has high efficiency.
a) Find the probability of event A.
b) Find the probability of event B.
c) Find the probability of the intersection of A and B.
d) Are events A and B independent? Explain your answer.
Explanation / Answer
a) P(A) = 2/10 = 1/5
b) P(B) = (2/10)x(1/9) + (8/10)x(2/9) = 1/5
c) P(A intersection B) = (2/10)x(2/9) = 2/45
d) P(A) x P(B) = 1/25
So, P(A) x P(B) is not equal to P(A intersection B)
Hence, the events are not independent