prob. plane's alternators fail; lifetime prob. of fatal acci

[Mistyblu348]

Good afternoon everyone and thank you in advance for your help!

I have a friend that needs help with a couple of probability problems. Although, I am a college instructor, my expertise does not lie here! So... I thought I would enlist some assistance...here are the problems:

1: A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail in a 1-hour flight is .02. What is the probability that (a) both will fail ?(b) Neither will fail? (c) one or the other will fail?

2: The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50, 000 trips. (a) what is the probability of a fatal accident over a lifetime? Explain your reasoning. Hint: Assume independent events. why might the assumptions of independence be violated? (b) why might a driver be tempted not to use a seat belt :just on this trip"?

Any assistance would be greatly appreciated! I am such a liberal arts person and math is soo beyond me!

Mistyblu348

 

[Deleted member 4993]

I have a friend that needs help with a couple of probability problems. Although, I am a college instructor, my expertise does not lie here! So... I thought I would enlist some assistance...here are the problems:

1: A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail in a 1-hour flight is .02. What is the probability that (a) both will fail ?(b) Neither will fail? (c) one or the other will fail?

2: The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50, 000 trips. (a) what is the probability of a fatal accident over a lifetime? Explain your reasoning. Hint: Assume independent events. why might the assumptions of independence be violated? (b) why might a driver be tempted not to use a seat belt :just on this trip"?

I suggest you tell your friend to share her work/thoughts with us - so that we know where to begin to help her.

Being an instructor, I am sure you know that we cannot begin to help your friend learn this topic - unless we know where she is stuck!

 

[Mistyblu348]

Thank you for such a timely response. She has actually no clue where to begin....however, I can share with you my thoughts on how this might be tackled.

Hmm...for the first one, there are two (2) independent alternators, the probability of either of them failing is .02. So for starters, and I know I am probably totally wrong, I would:

P(2) = you two possible choices, either of them failing which would be 1.
P(1)=P(1) would equal 1/2 a 50/50 chance that either of them would fail.
Now I am lost on the idea that neither of them would fail as I fear that I am missing using the .02 someplace.

Question #2:Here is my feeble attempt...1 in 4,000,000 fatal accidents over a lifetime. 50,000 trips by U.S. drivers over a lifetime. So I would make it simple, and again this is probably totally wrong but, I would divide the 4,000,000 by the 50, 000 and come up with a probability of 80%. Hmm...again, I am not sure if I am over simplifying or not.

Please advise.

 

[Deleted member 4993]

These are standard problems - there must be similar problems solved in the textbook.

If you google "a single auto trip in the United States will result in a fatality" - you will find that this exact problem has been solved many time over.

Similarly the second problem.

If your friend has no-clue where to start - why is s/he is taking a class in this (where s/he is unwilling to put the effort to work through example problems in the text book and is asking you to help) topic?

 

[Mistyblu348]

I am not sure why she asked for my assistance. I would assume that math intimidates her as it does many. I will take your suggestion and send her the help!

Have a great night!

 

[stapel]

I am not sure why she asked for my assistance.... I will take your suggestion and send her the help!

Excellent!

As of course you, as an instructor, well understand, attempting to work through a "translator" who admittedly does not "speak the language" has almost no chance of success, and of course you wish your friend all success. Once the tutors can communicate directly with your friend, they will be able to provide whatever help is needed. :wink:

Thank you!

Eliz.