A lot of 10 components contains 3 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective.
a. Find P(A).
b. Find P(B|A).
c. Find P(A ? B).
d. Find P(
? B).
e. Find P(B).
f. Are A and B independent? Explain.
(a) P(A) = 3?10
(b) Given that A occurs, there are 9 components remaining, of which 2 are defective.
Therefore P(B|A) = 2?9.
(c) P(A ? B) = P(A)P(B|A) = (3?10)(2?9) = 1?15
(d) Given that 
occurs, there are 9 components remaining, of which 3 are defective.
Therefore P(B|A) = 3?9. Now 
= (7?10)(3?9) = 7?30.
(e) P(B) = P(A ? B) + P(? B) = 1?15 + 7?30 = 3?10
(f) No. P(B) ? P(B|A) [or equivalently, P(A ? B) ? P(A)P(B)].
You might also like to view...
What is the main reason VCO nozzle geometry has become common today?
A. lower manufacturing costs B. lower HC emissions C. lower NOx emissions D. easier to recondition
Technician Asays water trapped around brake tubes, fittings, and mounting clips can rust and corrode steel tubing. Technician B says mounting clips can trap salt water and hide severe corrosion. Who is correct?
A. A only B. B only C. Both A and B D. Neither A nor B
A solid material exerts a pressure or force ____.
A. in all directions B. downward only C. outward and downward D. outward only
Sketch the magnitude frequency response of the systems in Figure E.23 from their pole-zero diagrams.
