SOLUTION: Hi Please help me the following problems 1. Every time a particular circuit is turned on there is a chance that one or more of its components will fail. The probability that non

Question 783276: Hi Please help me the following problems
1. Every time a particular circuit is turned on there is a chance that one or more of its components will fail. The probability that none of the components fail is 0.35. The probability that exactly one of the components fail is 0.39, and the probability that all the components fail is 10−10.
a. Find the probability that at most one of the components fails.
b. Find the probability that at least one of the components fails.
c. Find the probability that at least one of the components functions properly.
2. Two people are selected at random from a group of 8 women and 12 men. Consider the following events.
A = {1st person is a woman}
B = {2nd person is a woman}
C = {1st person is a woman and the second is a man}
D = {1st person is a man and the second is a woman}
E = {Exactly one of the two people selected is a woman}
a. Find P(A), P(B), and P(B/A).
b. Are A and B independent? Are they mutually exclusive?
c. Find P(C) and P(D).
d. How is E related to C and D?
e. Find P(E).
3. Widgets coming off an assembly line have a 10% defective rate. Five widgets are selected at random and tested.
a. What is the probability that all five of them are defective?
b. What is the probability that the first two are defective and the other three are not?
c. What is the probability that the second and fifth ones are defective and the other three are not?
d. How many different outcomes result in exactly two of the five being defective?
e. What is the probability that exactly two of the five are defective?
4. In a certain video game, a submarine can fire five torpedoes at a time. If the probabilities of the first, second, third, fourth and the last torpedo hitting the enemy ship are 0.7, 0.6, 0.5, 0.4 and 0.3.
What is the probability that five torpedoes aimed at an enemy ship will sink the ship?
5.When a fish is hooked and then released there is a 5% chance that it will die. Suppose a group of anglers goes fishing and releases a total of 20 fish.
a. What is the probability that the 1st, 2nd, and 3rd fish released all die and the rest survive?
b. What is the probability that the 5th, 16th, and 17th fish released all die and the rest survive?
c. How many outcomes result in exactly three of the fish dying and the rest surviving?
d. What is the probability that exactly three of the fish die?
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
The rule of the forum is one question per post. Anyway, if you need the solution for this assignment then send me an email.
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