I need help with two word problems that have to do with probability. Can someone please help me?
Some of us might be able to if you tell us the problems.
Thank you and here is the two problems.
1. A certain airplane has two independent alternators to provide electrical power. The probability that a certain given alternator will fail on 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? Show all steps.
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 assumption of independence be violated? (b)Why might a driver by tempted to not use a seat belt "just on this trip"?
Can you please help me with both of these problems as I am not sure how to solve them? Thank you for any and all help.
1. Multiply the probabilities of the separate outcopmes for each.
The probability that both will fail is (0.02)^2 = 0.0004
The probability that #1 will fail and #2 will not is 0.02*0.98 = 0.196
The probability that #2 will fail and #1 will not is also 0.01960
You need to add the last two results to get the probability that one will fail: 0.0392
The probability that neither will fail is (0.98)^2 = 0.9604
Note that the total is 0.0004 + 0.0392 + 0.9604 = 1.0000
2. The probability of surviving each trip is 1 - 4*10^-6 = 0.999996.
Take the 50,000 power of that as the probability of surviving 50,000 trips in a row with no fatality to anyone. That is 0.819. (The number seems too low - about 5% of people in the United States die in accidents; not 18%. But that is what you get using their numbers and "independent event" assumptions)
Trips are not really independent since the probability of a fatality on any trip varies with the driver's age, state of residence, time of day/night, weather conditions and the length of the trip.
(b) Some people might expect the probability of being injured in a short off-highway trip, or one in light traffic, to be less, and not want to bother with the seat belt in such a case. Statistics may prove such trips are more dangerous. (I don't know)
Please excuse the multiple identical answers above. There was something wrong with Jiskha's operation this morning.
Thank you so very much for helping me with the two problems. I can now finish the rest of my homework. Take care and thanks for helping me and other students like me.
1.
a) 0.02*0.02= 0.04
b) 1-0.04= 0.06
c) 0.02*0.08= 0.0016