The probability that Sarah takes one piece of each fruit is; (10x - x²)/100
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We are given;
- Number of fruits in the bowl = 10
Thus, remaining fruits are;
- Number of apples = 10 - x
Probability that at least one will be banana = x/10
Probability that at least one will be apple = (10 - x)/10
Thus;
Probability that she takes one piece of each fruit is;
x/10 × (10 - x)/10
⇒ x(10 - x)/100
⇒ (10x - x²)/100
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Answer:

Step-by-step explanation:
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Answer:
a) The mean number of cases is 0.14608 cases.
b) The probability that the number of cases is exactly 0 or 1 is 0.990.
c) The probability of more than one case is 0.010
d) No, because the probability of more than one case is very small
Step-by-step explanation:
We can model this problem with a Poisson distribution, with parameter:

a) The mean amount of cases is equal to the parameter λ=0.14608.
b) The probability of having 0 or 1 cases is:

c) The probability of more than one case is:

d) The cluster of 4 cases can not be due to pure chance, as it is a very high proportion of cases according to the average rate. Just having more than one case has a probability of 1%.