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Probability of Correctly Selecting Winning Lottery Numbers

A certain state is contemplating creating a weekly lottery, the revenues from which will be used to fund improvements in the state's public education system. The commission chartered to develop the guidelines for the proposed lottery envisions using a process whereby six (6) balls will be randomly selected from a single bin containing a total of forty (40) balls, each of which is individually numbered 1 through 40, in order to determine the winning lottery numbers each week. Once a given ball has been randomly selected it will not be placed back in the bin before selecting the next ball. The commission is currently debating whether an individual should be required to pick the winning lottery numbers in a specific order or be allowed to pick them in a random order.

18. Assuming that the order in which the winning lottery numbers are selected is irrelevant (i.e., not important), what is probability of someone correctly selecting the six (6) winning lottery numbers?
a. 2.6 x 10-7
b. 1.5 x 10-1
c. 3.6 X 10-10
d. 7.1 X 10-8

19. Assuming that the order in which the winning lottery numbers are selected is relevant (i.e., is important), what is probability of someone correctly selecting the six (6) winning lottery numbers?
a. 1.5 x 10-1
b. 2.6 x 10-6
c. 3.6 X 10-10
d. 7.1 X 10-8.

Solution Summary

The solution determines the probability of correctly selecting six winning lottery numbers.

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