1. ## Probability/Statistics

Hi everyone,

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:
a) .04
b) 0
c) .02

Is this correct or am I missing something. I would greatly appreciate the help! Thanks in advance!

2. $\begin{array}{l}
a)\quad \left( {.02} \right)\left( {.02} \right) \\
c)\quad \left( {.02} \right) + \left( {.02} \right) - \left( {.02} \right)^2 \\
\end{array}$

Can you explain these?

3. ## Probability/Statistics

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!