Help with 3 probability exercises

sback

New member
Joined
Oct 1, 2016
Messages
1
First problem: There are 10 members of the management board of a company. They choose the "leaders" of the company - a president, a vice president and a secretary. Find the probability out of 3 members of the management board:
a)3 of them to be hired as leaders;
b)none of them to be hired as leaders;
c)2 of them to be hired as leaders;
d)maximum 2 of them to be hired as leaders.

Second problem: A machine consists of two elements. The operation of each element is unconditionally needed for the operation of the machine. The probability of a flawless operation, during the period of time T, for the first element is - 0.8 and for the second - 0.9. The machine is tested for a period of time T. The results show that the machine has stopped operating. Find the probability only the first element to have broken(stopped working) while the second one has worked flawlessly during the test.

Third problem:
An electrical applience works in two modes - lightly loaded and heavily loaded. The applience is lightly loaded for 7 hours and heavily loaded for 17 hours in the period of 24 hours. The probability the applience to break when it's lightly loaded is 0.001 and while heavily loaded - 0.01. Determine the reliability of the applience during a period of 24 hours.
 
First problem: There are 10 members of the management board of a company. They choose the "leaders" of the company - a president, a vice president and a secretary. Find the probability out of 3 members of the management board:
a)3 of them to be hired as leaders;
b)none of them to be hired as leaders;
c)2 of them to be hired as leaders;
d)maximum 2 of them to be hired as leaders.

Second problem: A machine consists of two elements. The operation of each element is unconditionally needed for the operation of the machine. The probability of a flawless operation, during the period of time T, for the first element is - 0.8 and for the second - 0.9. The machine is tested for a period of time T. The results show that the machine has stopped operating. Find the probability only the first element to have broken(stopped working) while the second one has worked flawlessly during the test.

Third problem:
An electrical applience works in two modes - lightly loaded and heavily loaded. The applience is lightly loaded for 7 hours and heavily loaded for 17 hours in the period of 24 hours. The probability the applience to break when it's lightly loaded is 0.001 and while heavily loaded - 0.01. Determine the reliability of the applience during a period of 24 hours.


Please post one problem in one post.

Please include your work, explaining exactly where you are stuck.
 
Help with 3 probability exercises
We'll be glad to try to help! But first, we'll need to see where you're stuck. (For instance, if you have no idea what any of these exercises is talking about, our "help" would have to be to advice you to consider enrolling in a course in probability and statistics, since there's way too much you would need to learn first, before we'd be at all able to assist with these particular exercises.)

1. There are 10 members of the management board of a company. They choose the "leaders" of the company - a president, a vice president and a secretary. Find the probability out of 3 members of the management board:
a)3 of them to be hired as leaders;
b)none of them to be hired as leaders;
c)2 of them to be hired as leaders;
d)maximum 2 of them to be hired as leaders.
Have you copied this exercise exactly as it appears in the original assigment? Or was there additional information, such as the pool from which they're doing the choosing? (Without that info, we can't solve this, either. If we assume that they choose the "leaders" from amongst themselves only, then parts (a) and (b) are trivial, while part (d) is impossible -- so, in a sense, also trivial, but...)

2. A machine consists of two elements. The operation of each element is unconditionally needed for the operation of the machine. The probability of a flawless operation, during the period of time T, for the first element is - 0.8 and for the second - 0.9. The machine is tested for a period of time T. The results show that the machine has stopped operating. Find the probability only the first element to have broken(stopped working) while the second one has worked flawlessly during the test.
Did the original exercise contain those "minus" signs in front of each of the probabilities? If so, what on earth does your book mean by this notation? If not, what was the text of the original exercise?

3. An electrical appliance works in two modes - lightly loaded and heavily loaded. The appliance is lightly loaded for 7 hours and heavily loaded for 17 hours in the period of 24 hours. The probability the appliance to break when it's lightly loaded is 0.001 and while heavily loaded - 0.01. Determine the reliability of the appliance during a period of 24 hours.
Okay; I'll guess that your book really does have a "minus" sign in front of the indicated probabilities, because it does not have a "minus" sign in front of the "lightly-loaded" probability. Please reply with your book's definition for whatever this is meant to be.

When you reply, please include a clear listing of your thoughts and efforts so far. Thank you! ;-)
 
Top