ISYE 3770_Quiz1_sol
ISYE 3770 B
Wednesday Jan 22
Quiz 1
Your name (please print): Solution Key
1.
Consider the following hybrid reliability system. The number in each box indicates the component’s reliability (probability of working). Assume components fail independently. What is the probability that the entire system works? (only write down the expression)
P(works) = P(A)*P(B) + P(C)*P(D)*P(E) – P(A)*P(B)*P(C)*P(D)*P(E)
= 0.7*0.7 + 0.8*0.8*0.8 – 0.7*0.7*0.8*0.8*0.8
2.
Finish the following Bayes theorem (only the basic version, not with total probability rule):
For two events A and B, with P(A) > 0 and P(B) > 0,
P(A|B) = P(B|A) * P(A) / P(B)
3.
The probability that a regularly scheduled flight departs on time is P(D)=0.83; the probability that it arrives on time is P(A)=0.82; and the probability that it arrives on time given that it departed on time is
P(A|D)=0.94. Find the probability that a plane departs on time given that it arrives on time. (only write down the expression)
P(D|A) = P(A|D)*P(D) / P(A) = 0.94*0.83 / 0.82
4.
A box contains 3 blue and 2 red pens while another box contains 2 blue and 5 red pens. A pen drawn at random from one of the boxes turns out to be blue. What is the probability that it came from the first box?
(only write down the expression)
P(first|blue) = P(blue|first) * P(first)/P(blue)
= [3/(3+2) ]* [(3+2)/(3+2+2+5)] / [(3+2)/(3+2+2+5)]
5.
A random variable must be: (1) random, (2) variable (i.e. a number that is not fixed). So which of them are random variables? (cycle the letters) – Answers are c and d.
(a)
(b)
(c)
(d)
result of flipping a fair coin the number 50 total number of “head” results when you flipping a fair coin for 50 times the variable X, where X = 1 if we get a “head” when flipping a fair coin; X = 0 otherwise
Wednesday Jan 22
Quiz 1
Your name (please print): Solution Key
1.
Consider the following hybrid reliability system. The number in each box indicates the component’s reliability (probability of working). Assume components fail independently. What is the probability that the entire system works? (only write down the expression)
P(works) = P(A)*P(B) + P(C)*P(D)*P(E) – P(A)*P(B)*P(C)*P(D)*P(E)
= 0.7*0.7 + 0.8*0.8*0.8 – 0.7*0.7*0.8*0.8*0.8
2.
Finish the following Bayes theorem (only the basic version, not with total probability rule):
For two events A and B, with P(A) > 0 and P(B) > 0,
P(A|B) = P(B|A) * P(A) / P(B)
3.
The probability that a regularly scheduled flight departs on time is P(D)=0.83; the probability that it arrives on time is P(A)=0.82; and the probability that it arrives on time given that it departed on time is
P(A|D)=0.94. Find the probability that a plane departs on time given that it arrives on time. (only write down the expression)
P(D|A) = P(A|D)*P(D) / P(A) = 0.94*0.83 / 0.82
4.
A box contains 3 blue and 2 red pens while another box contains 2 blue and 5 red pens. A pen drawn at random from one of the boxes turns out to be blue. What is the probability that it came from the first box?
(only write down the expression)
P(first|blue) = P(blue|first) * P(first)/P(blue)
= [3/(3+2) ]* [(3+2)/(3+2+2+5)] / [(3+2)/(3+2+2+5)]
5.
A random variable must be: (1) random, (2) variable (i.e. a number that is not fixed). So which of them are random variables? (cycle the letters) – Answers are c and d.
(a)
(b)
(c)
(d)
result of flipping a fair coin the number 50 total number of “head” results when you flipping a fair coin for 50 times the variable X, where X = 1 if we get a “head” when flipping a fair coin; X = 0 otherwise