Question

The probability that a house in an urban area will be burglarized is 3 1 57 houses are randomly selected, what is the probability that none of the houses will be burgare OM 0.176 OB. 0.030 oc. ooo1 OD 0.000

Answer 1

Solution:

Given:

p = probability of a house in a urban area will be burglarized  = 3% = 0.03

n = Number of houses randomly selected.

We have to find:

P( None of the house in a urban area will be burglarized)= ...........?

P( X=0) =............?

Using Binomial probability formula :

P(X = x) =n Cx pul xqN-1

Where

n! nort! x (n-1)!

q = 1 - p = 1 - 0.03 = 0.97

Thus

P(X=0) =57 Co x 0.030 x 0.9757-

57! P(X = 0) = 1 AT O 0! < (57 – VX1X 0.9757 ! (57 – 0)!“

57! P(X =0) = 1 x 57! X1x 0.17619

P(X =0) = 1x1 x 0.17619

P(X = 0) = 0.17619

P(X =0) = 0.176

Thus correct answer is: A. 0.176