A large number of spoons and forks made in a factory are inspected. It is found that \(1 \%\) of the spoons and \(1.5 \%\) of the forks are defective. A random sample of 140 items, consisting of 80 spoons and 60 forks, is chosen. Use the Poisson approximation to the binomial distribution to find the probability that the sample contains
at least 1 defective spoon and at least 1 defective fork,
fewer than 3 defective items.
The random variable \(X\) has the distribution \(\operatorname { Po } ( \lambda )\). It is given that
$$\mathrm { P } ( X = 1 ) = p \quad \text { and } \quad \mathrm { P } ( X = 2 ) = 1.5 p$$
where \(p\) is a non-zero constant. Find the value of \(\lambda\) and hence find the value of \(p\).