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Math Help - Probability/Statistics

  1. #1
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    Exclamation 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!
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  2. #2
    MHF Contributor

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    \begin{array}{l}<br />
 a)\quad \left( {.02} \right)\left( {.02} \right) \\ <br />
 b)\quad (.98)^2  \\ <br />
 c)\quad \left( {.02} \right) + \left( {.02} \right) - \left( {.02} \right)^2  \\ <br />
 \end{array}
    Can you explain these?
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  3. #3
    Newbie
    Joined
    Jan 2008
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    Lightbulb 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!
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