SOLUTION: In a lottery game, a player picks six numbers from 1 to 53. If 5 of the 6 numbers matches those drawn, the player wins $1000. What is the probability of winning this prize?
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-> SOLUTION: In a lottery game, a player picks six numbers from 1 to 53. If 5 of the 6 numbers matches those drawn, the player wins $1000. What is the probability of winning this prize?
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Question 1162122: In a lottery game, a player picks six numbers from 1 to 53. If 5 of the 6 numbers matches those drawn, the player wins $1000. What is the probability of winning this prize? Answer by Edwin McCravy(20054) (Show Source):
The player can pick all 6 winning numbers in 6C6 = 1 way
The player can pick 5 winning numbers and 1 non-winning number in (6C5)∙(47C1) = 282 ways.
So there are 1+282=283 ways the player could win.
There are 53C6 = 22957480 ways the player could pick 6 numbers.
Probability of winning = 283 ways out of 22957480 or 283/22957480 or about
0.000012327136950571229943356152330308030323885722649001545...
1.2327×10-5, which is about 1 chance in 81122.
Edwin
