1. ## Statistics HomeWork Urgent

A dog will shed and a hair will fall in your food with probability .35 on any given day.
Find the probability that in a month with 30 days there will be 10 or less days that have dog hair in your food.

2. Hi civiliam.

Originally Posted by civiliam
A dog will shed and a hair will fall in your food with probability .35 on any given day.
Find the probability that in a month with 30 days there will be 10 or less days that have dog hair in your food.
In this case you got to use the binomial distribution with p=0.35 so it is 1-p = 1 - 0.35 = 0.65

So have to calculate

Probability("on 30 days there is no hair on your food") = $\displaystyle \begin{pmatrix} 30 \\ 0 \end{pmatrix}0.35^0*0.65^{30}$

Probability("on 30 days you find on one day a hair")= $\displaystyle \begin{pmatrix}30 \\ 1\end{pmatrix}0.35^1*0.65^{29}$

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Probability("on 10 days out of 30 you find some hair") = $\displaystyle \begin{pmatrix}30 \\ 10\end{pmatrix}0.35^{10}*0.65^{20}$

And now you have to add all this probalilities to find probability(10 or less times you find some hair in 30 days) = prob(no hair was found) + prob(one time hairs were found) + prob(two times hairs were found) +prob(three times hairs were found) + ... + prob(ten times hairs were found)

Yours
Rapha