SOLUTION: I am not grasping probability at all! I'm 36 years old and I have just returned back to school. Can you please help? A certain airplane has two independent alternatiors to pro

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Question 192160: I am not grasping probability at all! I'm 36 years old and I have just returned back to school. Can you please help?
A certain airplane has two independent alternatiors to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02.
What is the probability that (a) both fail? (b) neither will fail? (c) One or the other will fail? Show all steps carefully.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
a) The probability of both engines failing is simply the product of the individual probabilities. So...

p(both failing) = p(one failing)*p(other failing)
p(both failing) = 0.2*0.2
p(both failing) = 0.04

So the probability of both failing is 0.04 which is 1/25 or 4%

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b) The probability of neither failing is the same as the probability of both NOT failing. So in this part, we're multiplying the probabilities of both engines NOT failing to get:

P(neither failing) = p(one NOT failing)*p(other NOT failing)
P(neither failing) = (1-0.2)*(1-0.2)
P(neither failing) = 0.8*0.8
P(neither failing) = 0.64

So the probability of neither failing is 0.64 which is 16/25 or 64%

Note: if x is the probability of an event occurring, then 1-x is the probability of the event NOT occurring.
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c) To find the chances if one event or the other occurs, simply add the two individual probabilities and subtract out the probability that they will both occur (to remove duplicates):

P(one or other failing) = p(one failing) + p(other failing) - p(both failing)
P(one or other failing) = 0.2 + 0.2 - 0.04
P(one or other failing) = 0.36

So the probability of either one failing (but not both) is 0.36 which is 9/25 or 36%