# Probability

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A state runs a lottery in which 6 numbers are randomly selected from 40, without replacement. A player chooses 6 numbers before the state's sample is selected.

a. What is the probability that the 6 numbers chosen by the player match all 6 numbers in the state's sample?

b. What is the probability that 5 of the 6 numbers chosen by the player match all 6 numbers in the state's sample?

c. What is the probability that 4 of the 6 numbers chosen by the player match all 6 numbers in the state's sample?

d. If the player enters one lottery each week, what is the expected number of weeks until a player matches all 6 numbers in the state's sample?

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##### Solution Summary

The probability of randomly selected numbers are determined. Neat, Step-by-step solution is provided.

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The 6 numbers can be selected out of 40 numbers, without replacement in 40C6 ways = 3838380 ways. This means there

are 3838380 possible selections.

(a) All the six numbers selected by a player can match the six drawn by the state in just one way

Therefore, ...

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