Question 1025792: In a certain city district, the need for money to buy drugs is given as the reason for 65% of all thefts. What is the probability that exactly 2 of the next 4 theft cases reported in this district resulted from the need for money to buy drugs?
Answer by mathmate(429)   (Show Source):
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Question:
In a certain city district, the need for money to buy drugs is given as the reason for 65% of all thefts. What is the probability that exactly 2 of the next 4 theft cases reported in this district resulted from the need for money to buy drugs?
Solution:
We know that the experiment consists of 4 Bernoulli (true or false) trials, with a constant probability of 0.65. We further assume that the (next) cases are random and independent of each other. This way, the situation can be modelled by the binomial distribution, having
p=0.65,
n=4
k=2 (number of "successes", meaning drug related motive).
with a probability of
P(k,n,p)=
where
C(n,k)=n!/(k!(n-k)!)
Substituting values,
P(2,4,0.65)
=6*0.4225*0.1225
=0.3105375
=0.311 (rounded to 3 sig. figures)
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