assuming all the conditions are fulfilled (independent trials, two possible outcomes per trial that can be thought of as success or failure ...), we have the following by the method of Bernoulli trials.
the probability of successes in trials, where the probability of success is and the probabilty of failure is is given by:
so for question (1), you have:
for (a) you want
for (b) you want
for (c) you want
for question one, it was also possible to reason through it.
part (a) is asking the probability that alternator 1 will fail AND alternator 2 will fail. since we have independent trials, we can just multiply the probabilities
part (b) is asking the probability that alternator 1 does not fail AND the probability that alternator 2 does not fail, again, we just multiply the respective probabilities
part (c) is asking for the probability the alternator 1 fails but 2 doesn't OR the probability that alternator 1 does not fail, but 2 does. we can ADD the probabilities for each case here, since we have OR as opposed to AND
for question (2), you have:
for the first part of part (a), you simply want . for the second part, you could say the car accidents might not be independent, but one accident can cause another...what other way can you think of that the accidents may not be independent?
for part (b), answer part (a) and you should have it