Question

There are currently 18 pit bulls at the pound. Of the 18 pit bulls, four have attacked another dog in the last year. Joe, a member of the staff, randomly selects six of the pit bulls for his group.

a. What is the probability that at least one of the pit bulls in Joe’s group attacked another dog last year?

b. What kind of distribution is this?

Answer 1

a)

x items are selected from n items by ⁿC_x ways.

ⁿC_x = n! / [ ( n - x)! * x! ]

Where X is number of pit bulls in Joe’s group attacked another dog.

Of the 18 , 4 attacked another dog and 14 does not attacked another dog.

P(X >= 1) = 1 - P(X = 0)

= 1 - [^18-4C₆ / ¹⁸C₆ ]

= 1 - [ ¹⁴C₆ / ¹⁸C₆ ]

= 1 - 0.1618

= 0.8382

b)

This is hyper geometric distribution.