Question

In: Statistics and Probability

In a certain​ lottery, an urn contains balls numbered 1 to 37. From this​ urn, 4...

In a certain​ lottery, an urn contains balls numbered 1 to 37. 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?

Solutions

Expert Solution

Number of ways 4 balls are chosen​ randomly, without replacement (when order in which the balls are selected does not matter)  = 37C4

= 37! / [(37 - 4)! * 4!]

= 37! / (33! * 4!)

= (37 * 36 * 35 * 34) / (4 * 3 * 2 * 1)

= 66045

For a​ $1 bet, a player can choose only one set of four numbers out of 66045 sets.

So, the probability of winning this lottery with one​ ticket = 1 / 66045

orchestra answered 2 years ago
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