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probability and relative probability question showing work to receive credit.

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a doctor discovered cases of chicken pox happen 8 times in the past 3 years.  What is the relative frequency probability that a case of chicken pox will happen again in 1 year?  What is the probability the chicken pox will occur in any given year?

Sep 25th, 2017

The relative frequency probability is simply an estimated probability based on the frequency of the event in the past: So in this case the relative frequency of chicken pox is 8 cases per 3 years; so a mean number of cases per year is estimated to be 8/3. 

The question asks us what the chance is that we'll see a case of chicken pox in the next year. Since we're talking about discrete events occurring during some time frame, a sensible approach might be to use the Poisson distribution (with a mean, i.e. lambda, of 8/3). Since we can't have a negative number of cases, the probability of seeing at least one case of chicken pox in the next year can be calculated by 1 minus the probability of no cases (X=0):

Pr(X>0) = 1 - Pr(X=0) = 1 - ( [ lambda^0 * e^(-lambda) ] / 0! )

= 1 - ( [ 1 * e^(-8/3) ] / 1 )

= 1 - e^(-8/3) 

= 0.9305; around a 93% probability of seeing at least one case.

(I interpret both of the questions as asking for that probability, but they're not entirely clear).


Hope this helps!

Feb 27th, 2015

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