The multi-state Powerball lottery requires each ticket buyer to select the numbe
ID: 3353879 • Letter: T
Question
The multi-state Powerball lottery requires each ticket buyer to select the numbers for 5 "white balls" and 1 "red ball". The winning numbers are selected by random by the lottery's computer. For the white balls, the number can vary between 1 and 69; however, the number can only be used once. So once the number is selected, it can not be chosen for another ball, i.e. 5 different numbers for the white balls. The red power ball's number can be between 1 and 26. A winner of the lottery needs to "select" the 5 white ball numbers, in any order, plus the correct number for the red ball. What are the odds of winning?
One writer claimed that the odds of winning the Powerball lottery are almost the same as tossing 27 consecutive heads (with a fair coin). Is he correct?
a) The odds of winning the Powerball lottery are ____________
b) the odds of tossing 27 consecutive heads with a fair coin are __________________
Explanation / Answer
a) Total number of combinations possible for drawing red and white balls = 69C5 * 26C1 = 292201338
In this, there would be only 1 winning number. Hence,
P(Winning) = 1/292201338
Odds of winning = 1 : 292201337
b) P(27 consecutive heads) = (1/2)27 = 1/134217728
Hence,
Both the given probabilities are not equal.