POWERBALL game contains two sets of numbers: One set from 1 through 69 and the s

Question

POWERBALL game contains two sets of numbers: One set from 1 through 69 and the second set from 1 through 26. A player need to select five numbers from the first set and one number from the second set.

a) The second prize - won by just matching the first five numbers in any order to the later five numbers drawn is $1,000,000 paid in cash (no annuity option).

What is the probability that the first five selected numbers match the five number that are later drawn?

b) Any time the player match the Powerball, the number picked from the second set, to the later number drawn from the second set, the player wins $4.

What is the probability that the sixth selected number matches the sixth number that is later drawn?

c) The jackpot, starting from 40 million, won by matching the first five numbers picked (in any order) to the same five numbers that are later drawn, and the sixth number must also match the sixth number that is later drawn.

What is the probability of winning the jackpot?

Explanation / Answer

There are 69 numbers in the 1st set

There are 26 numbers in the 2nd set

a) The probability that the first five selected numbers match the five number that are later drawn

There are C(59,5) ways of choosing 5 balls from 59

Number of ways=11,238,513

The number of ways your 5 numbers match the selected 5 numbers=C(5,5)=1

Probability that the first five numbers matches =1/11,238,513=0.00000008898

b) The probability that the sixth selected number matches the sixth number that is later drawn

There are C(26,1) ways for selecting 1 number from 26 numbers.

Number of ways=26

Number of ways of matching your powerball number with Single powerball number=C(1,1)=1

Probability that the 6th number matches=1/26=0.0385

c) The probability that the sixth selected number matches the sixth number that is later drawn

There are C(26,1) ways for selecting 1 number from 26 numbers.

Number of ways=26

Jackpot means matching first 5 numbers and the powerball.

Total number of ways=C(69,5)*C(26,1)=292,201,338

Number of ways of winning jackpot=C(5,5)*C(1,1)=1

Probability of winning jackpot=1/292,201,338=0.000000003422

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