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.
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.
Hi civiliam.
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