Question

In a certain city​ district, the need for money to buy drugs is stated as the reason for 69%of all thefts. Find the probability that among the next 5 theft cases reported in this​ district, ​(a) exactly 2 resulted from the need for money to buy drugs. ​(b) at most 3 resulted from the need to buy drugs

Answer 1

Solution

Given that ,

p = 0.69

q = 1 - p = 1 - 0.69 = 0.31

n = 5

Using binomial probability formula ,

P(X = x) = (n C x) * p x * (1 - p)n - x

P(X = 2) = (5 C 2) * 0.692 * (0.31)3

=0.1418

probability=0.1418

(B)

P(X <3   ) = P(X=0) +P(X=1)+P(X=2)+P(X=3)

=(5 C 0) * 0.690 * (0.31)5+(5 C 1) * 0.691 * (0.31)4+(5 C 2) * 0.692 * (0.31)3+(5 C 3) * 0.693 * (0.31)2

probability =0.4923