A dairy farmer accidentally allowed some of his cows to graze in a pasture containing weeds that would contaminate the flavor of the milk from this herd. The farmer estimates that there's a a 9 9% chance of a cow grazing on some of the flavorful weeds. (a) Under these conditions, what is the probability that none of the 16 16 animals in this herd ate the tasty weeds? (b) Does the Poisson model give a good estimate of the probability that no animal ate the weed?

the required probability of is 0.1886

the approximate probability is 0.2052

Step-by-step explanation:

The farmer estimates that there's a a 9 9% chance of a cow grazing on some of the flavorful weeds

i.e P = 9.9% = 0.099

Let assume that X is a description of how the cows are grazing on some of the flavorful weeds.

The probability density function of the binomial distribution is :

a)

To calculate that the probability that none of the 16  animals in this herd ate the tasty weeds.

=

= 0.1886

Thus; the required probability of is 0.1886

b) To calculate the probability that no animal ate the weed.

By using Poisson approximation model:

               =

Hence; the approximate probability is 0.2052

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step-by-step explanation:

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step-by-step explanation: