9 Buttercups in a meadow are distributed independently of one another and at a constant average incidence of 3 buttercups per square metre.
- Find the probability that in 1 square metre there are more than 7 buttercups.
- Find the probability that in 4 square metres there are either 13 or 14 buttercups.
- Use a suitable approximation to find the probability that there are no more than 69 buttercups in 20 square metres.
- (a) Without using an approximation, find an expression for the probability that in \(m\) square metres there are at least 2 buttercups.
(b) It is given that the probability that there are at least 2 buttercups in \(m\) square metres is 0.9 . Using your answer to part (a), show numerically that \(m\) lies between 1.29 and 1.3.