|Posted: March 24, 2015, 8:40 pm - IP Logged|
The Mega/Power ball will match one of the white balls about 6.7% of the time on Mega Millions, 8.5% on Powerball.
The exact probability can be calculated as follows (I'm using MM for the explanation; PB can be calculated by changing the numbers to reflect the pool size of 59 instead of 75):
Whatever the Mega ball is, the probability that the first white ball drawn will not match it is 74/75.
The probability that the second will also not match it is 73/74
The third, fourth and fifth are 72/73, 71/72, and 70/71.
So the probability that none of the five will be the same as the Mega ball is (75/74)*(73/74)*(72/73)*(71/72)*(70/71) = 70/75 ≈ 0.933.
The probability that one of them will match is therefore about 0.067, or 6.7%.
A lot of other things about the lottery can be calculated in similar ways.