Question

A shipment of 8 parrots from Brazil includes 2 parrots with a potentially fatal disease. As usual, the U. S. Customs Office at the shipment's point of entry randomly samples 4 parrots and tests them for disease. What is the probability that the first three parrots selected are healthy

Answer 1

Answer:

5 / 14

Step-by-step explanation:

Given that:

Number of parrots shipped = 8

Number of defective parrots = 2

Number of Random samples tested = 4

Number of healthy parrots = 8 - 2 = 6

Probability that first 3 parrots are healthy:

P(1st parrot) * p(2nd parrot) + p(3rd parrot)

P = (number of required outcomes / number of total possible)

USing sampling without replacement :

P(1st parrot healthy ) = 6/ 8 = 3/4

P(2nd parrot healthy) = 5 / 7

P(3rd parrot healthy) = 4 / 6 = 2/3

P(first 3 parrots being healthy) :

(3/4) * (5/7) * (2/3) = 30/84 = 5 / 14