Given that the number of emergency admission to a hospital each day has a Poisson distribution with mean 2.
1) The hospital has 4 bed for emergencies at the beginning of each day. Calculate the probability that the number is insufficient for that day.
2)Calculate the probability that there are exactly 3 emergency admission on two consecutive days.
For (1), I have no idea how to do, can someone show me a detailed working and explaination?
For (2), is it P(X=3) and once I got the answer, just multiply 2 because "2 consecutive days" ?
Thanks
For 1) you are asked for $P(X>4)$. The easiest way to do this, since it only involves a few terms, is to calculate the probability that this doesn't happen, then subtract from $1$.
For 2), you need to square it (not double it). The probability of two independent events both happening is obtained by multiplying the probabilities together, not adding them.