In a certain lottery game, you choose a set of four different integers between 1 and...

In a certain lottery game, you choose a set of four different integers between 1 and 50, inclusive, and a fifth integer between 1 and 20, inclusive, which may be the same as one of the other four.

a) What is the probability you win the jackpot by matching all five numbers drawn?

b) What is the probability that you match three of the first four numbers, but not the fifth?

This is for discrete math

Expert Solution

a) P(matching all 5 numbers) = P(matching the first four numbers) * P(matching the fifth number)

= (4C4 / 50C4) * (1/20)

= (1/230300) / (1/20)

= 1 / 4606000

b) P(matching 3 of first 4 numbers but not the fifth) = P(matching 3 of first 4 numbers ) * (1 - P(matching the fifth number))

= (4C3 * 46C1 / 50C4) * (1 - 1/20)

= (4 * 46 / 230300) * (19/20)

= 437 / 575750

orchestra answered 2 years ago

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