(a) Say that there is a 5% error rate in each experiment that a scientist does (ie that 5% of the time the scientist will think that they have a significant result when they don't or vice versa). On average, how many experiments will a scientist do before reaching their first false conclusion?

(b) You are tracking rabbits and observe one rabbit every 1.5 hours, on average. What is the probability that the first rabbit you see is in the last hour of an 8 hour day?

(c) You are trying to sequence a 500 basepair region of DNA, but you know that your method introduces sequencing errors at a rate of 0.001/basepair. What is the probability of obtaining the correct sequence entirely? What is the probability of getting exactly one error? What is the probability of getting more than one error?

(d) You are watching salmon swim by in a river and have, in the recent past, seen about one fish every ten minutes. You decide to wait for 10 fish to pass before heading home. How long do you expect to wait? What will the standard deviation of this estimate be? Since you realise that this is the sum of several independent events occurring, you decide it is reasonable to approximate the distribution using a normal distribution. From your statistics class, you remember that 95% of a normal distribution lies within 2 standard deviations of the mean. What is the 95% confidence interval in this case?