A distribution center receives shipment of a product from three different factories in the quantities of 60, 30 and 20. Three times a product is selected at random, each time without replacement. Find the probability that (a) all three products came from the second factory and (b) none of the three products came from the second factory
(a) The probability that all products came from the second factory is
(b) The probability that none of the three products came from the second factory is
(a) looks to me like it will be
(30/110)(29/109)(28/108)
Do (b) similarly.
This is just like the problems involving drawing from a deck of cards.
.019
To find the probability that all three products came from the second factory, we need to consider the total number of ways we can select three products from the three different factories. Since we are selecting without replacement, the first product can come from any of the three factories, the second product can only come from the second factory, and the third product can also only come from the second factory. So, the probability that all three products came from the second factory is:
(a) P(all three products came from the second factory) = (1/3) * (1/2) * (1/1) = 1/6 or approximately 0.1667
To find the probability that none of the three products came from the second factory, we can consider the number of ways we can select three products without any from the second factory. Since all the products from the second factory are excluded, we have to select all three products from the other two factories. So, the probability that none of the three products came from the second factory is:
(b) P(none of the three products came from the second factory) = (2/3) * (1/2) * (1/1) = 1/3 or approximately 0.3333