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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

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    for 1) do you know how to calculate the probability that the number of admissions is a certain value, such as 2 for example? The number is sufficient if you have 0,1,2,3, or 4 admissions - if you add the probabilities of those together, it gives the probability it IS sufficient, so then what is the probability it is NOT sufficient? – 2017-02-16
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    I understand it now! Thanks! – 2017-02-16

1 Answers 1

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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.

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    Noted with thanks ! – 2017-02-16