In a certain lottery, an urn contains balls numbered 1 to 34. From this urn, 4 balls are chosen randomly, without replacement

In a certain lottery, an urn contains balls numbered 1 to 34. From this urn, 4 balls are chosen randomly, without replacement. For a $1 bet, a player chooses one set of four numbers. To win, all four numbers must match those chosen from the urn. The order in which the balls are selected does not matter. What is the probability of winning this lottery with one ticket?

Expert Solution

An urn contains balls numbered 1 to 34

From the urn 4 balls are randomly chosen.

All four numbers must match to win.

Probability that first number will match = 4/34

Remaining balls in the urn after drawing the first ball are 33

Probability that second number will match = 3/33

Remaining balls in the urn after drawing the second ball are 32

Probability that third number will match = 2/32

Remaining balls in the urn after drawing the third ball are 31

Probability that fourth number will match = 1/31

Therefore, the probability of matching all four numbers to win this lottery with one ticket is

= (4/34) * (3/33) * (2/32) * (1/31)

= 0.000021

orchestra answered 2 years ago

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