Can you explain these?
I have been having trouble with this problem in my Statistics class. A certain airplane has two independent alternators 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 will fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully.
I think I have figured it out but I need some reassurance. The answers I got were:
Is this correct or am I missing something. I would greatly appreciate the help! Thanks in advance!
I will give it a try:
a) (.02)(.02) = .0004, probability that alternator 1 will fail AND alternator 2 will fail; therefore, I have to multiply the probabilities.
b) (.98)squared = 0.9604, probability that alternator 1 does not fail AND the probability that alternator 2 does not fail; therefore, I have to multiply the corresponding probabilities.
c) (.02) + (.02) - (.02)squared = .0396, probability alternator 1 fails but 2 does not OR probability alternator 1 does not fail but 2 does; therefore, I add the probabilities for each set because of the OR.
How is that? I think I am finally getting it. Thanks for giving me the push I needed to grasp this. I greatly appreciate it!