Question

**Please answer a and b**

Water in a reservoir is contaminated with a certain type of

bacteria which occurs according to

a Poisson Process with a mean rate of 2 bacteria every 10 liters. If you test one liter of water per day,

a) [5] what is the probability that you will find at least one of these bacteria in one week?

b) [5] what is the probability that the third bacteria found occurs within the first 4 litres tested

Answer #1

We are given the mean rate of bacteria here as 2 every 10 litres. Therefore in 1 litre, the mean rate is 2/10 = 0.2 The distribution here thus could be given as:

a) The probability that we will find at least one of these bacteria in one week that is 7 hours is computed here as:

**Therefore** **0.7534 is the required
probability here.**

b) Probability that the third bacteria found occurs within the
first 4 litres tested is computed here as:

= Probability that there are at least 3 bacteria in 4 litres of
water

**Therefore 0.0474 is the required probability
here.**

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