Not sure my reasoning is correct. Here is the question:
In a Nasa rocket firing, the probability of the siccess of the first stage is 95%, of the second stage 97% and of the third stage 98%. What is the probability of success for the three stage rocket?
My reasoning: There are three stages that the rocket has to go through to gain a success rate. So wouldnt it be the percentages added together then divided by 3, giving me 96%?
No, these are "dependent" events, so you multiply the probabilities.
so (.95)(.97)(.98) = ....
In your answer , look at it from a common sense point of view.
Since the prob of the first stage firing is .95, how can the prob that all three fire be higher than that ?
(you had .96)