In a lottery game, a machine has 48 balls marked with numbers from 1-48 and six of them are taken out at random. A player picks six of these numbers, trying to match the six balls that come out of the machine in any order. If exactly 4 of those 6 numbers match those drawn, the player wins third prize. What is the probability of winning this prize?
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In order to compute the probability, we need to count the total number of ways six numbers can be drawn, and the number of ways the six numbers on the player’s ticket could match the six numbers drawn from the machine. Since there is no stipulation that the numbers be in any particular order, the number of possible outcomes of the lottery drawing is 48C6 = 12,271,512. Of these possible outcomes, only one would match all six numbers on the player’s ticket, so the probability of winning the grand prize is:
c6c/48c6=1/12271512≈=0.0000000815
You answered the probability of matching all 6 balls.
The question is, if exactly 4 of those 6 numbers match those drawn, the player wins third prize. What is the probability of winning this prize?
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