A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fai
l on a one-hour flight is .02. a) What is the probability that both will fail?b) Neither will fail?c) One or the other will fail? Show all steps carefully.
When trying to find the probability of a sequence occurring you would simply need to multiply the probability of both of those things occurring together. Since the probability of an alternator failing is 0.02 then the probability of both failing would be...
0.02 * 0.02 = 0.0004
Now the probability of an alternator not failing is 0.98 (100% or 1 minus 0.02) therefore, the probability of both failing would be...
0.98 * 0.98 = 0.9604
Finally, the probability of one or the other failing would simply be the same as the probability of a single alternator failing which is 0.02
