Answer to Question #13862 in Statistics and Probability for Mike Mettler

Question

Total population size is 1052 objects. Group A contains 167 objects and Group B contains 885 objects. If objects are randomly drawn without replacement, how many objects must be drawn to obtain a probability of 90% that at least one of the objects belongs to Group A?

Answer 1

Probability that 1 object from group A selected:
P=167/1052=15.8%
Thus to have probability 90% we need to increase quantity of objects chosen in 90%/15.8%= 6 times
Thus we need to take 6 objects to have probability 90% of object A appearance