Revision
1. Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. Find the probability of the event that all 3 screws drawn are non defective, assuming that
we draw (a) with replacement, (b) without replacement.
2. In Problem 1 above, find the probability of obtaining at least 1 defective screw (a) directly, (b) by using complements.
3. If a box contains 10 left-handed and 20 right-handed screws, what is the probability of obtaining at least one right-handed screw in drawing 2 screws with replacement?
4. If a certain kind of tire has a life exceeding 40, 000 miles with probability 0.90, what is the probability that a set of these tires on a car will last longer than 40, 000 miles?
5. If a circuit contains four automatic switches and we want that, with a probability of 99%, during a given time interval the switches to be all working, what probability of failure
per time interval can we admit for a single switch?
6. A pressure control apparatus contains 3 electronic tubes. The apparatus will not work unless all tubes are operative. If the probability of failure of each tube during some interval
of time is 0.04, what is the corresponding probability of failure of the apparatus?
Probability Distributions (tutorial 2)
1. Graph the probability function f(x) = kx2 for x = 1, 2, 3, 4, 5 and constant k, and the frequency distribution.
2. Graph the probability function f(x) = kx2 for 0 ≤ x ≤ 5 and constant k, and the frequency distribution.
3. Graph f and F when the density of X is f(x) = ( k = const, −2 ≤ x ≤ 2 0, elsewhere. Find P(0 ≤ X ≤ 2).
4. A box contains 4 right-handed and 6 left-handed screws. Two screws are drawn at random without replacement. Let X be the number of left-handed screws drawn. Find the
probabilities (a) P(X = 0), (b) P(X = 1), (c) P(X = 2), (d) P(1 < X < 2), (e) P(X ≤ 1),(f) P(X ≥ 1), (g) P(X > 1), and (h) P(0.5 < X < 1)