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In a certain state's lottery, 45 balls numbered 1 through 45 are placed in a machine and seven of them are drawn at random. If the seven numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. In this lottery, the order in which the numbers are drawn does not matter.

Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket. Write your answer as a reduced fraction.

P P (win) = A single lottery ticket costs $2. Compute the Expected Value, to the state, if 10,000 lottery tickets are sold. Round your answer to the nearest dollar.

Answer: $ A single lottery ticket costs $2. Compute the Expected Value, to you, if you purchase 10,000 lottery tickets. Round your answer to the nearest dollar. Answer: $

Respuesta :

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Answer:

[tex]P(win) = \frac{1}{45,379,620}[/tex]

Expected value to the state if 10,000 tickets are sold = $19,780

Expected value to you if you purchase 10,000 tickets = -$19,780

Explanation:

Number of lotterry balls = 45

Number of balls drawn = 7

Win payout =  $1,000,000

Ticket cost = $2

a) Since the order does not matter, the number of total possibilities of choosing 7 balls out of 45 is:

[tex]_{45}C_{7}=\frac{45!}{(45-7)!7!} \\_{45}C_{7}=\frac{45*44*43*42*41*40*39}{7!} \\_{45}C_{7}=45,379,620[/tex]

Therefore, the probability of winning, P(win) by purchasing a single ticket is:

[tex]P(win) = \frac{1}{45,379,620}[/tex]

b) The expected value is given by the sum of the products of each outcome's pay by its likelihood. There are two outcomes, winning (which costs the state $1,000,000) and losing (which gives the state $2).

The expected value to the state if 10,000 tickets are sold is:

[tex]EV(N=10,000) = 10,000*EV(N=1)\\EV(N=10,000)=10,000*((2*\frac{45,379,620-1}{45,379,620})-(\frac{1}{45,379,620}*1,000,000))\\EV(N=10,000) = 10,000*1.9779636\\EV(N=10,000) = \$19,780[/tex]

The expected value, to the state, if 10,000 lottery tickets are sold is $19,780

c) The expected value to a player, for 'n' given games, is the opposite of the expected value to the state since each ticket costs $2 and the potential payout is $1,000,000 is case of victory. Therefore, the expected value, to a player, if they purchase 10,000 lottery tickets is -$19,780

The probability that an individual will win the million-dollar prize if one purchases a single lottery ticket will be 1/45379620.

How to calculate probability?

From the information given, the number of possibilities that one will choose 7 balls out of 45 will be:

= 45! / (45-7)!7!

= 45379620

Therefore, the probability is 1/45379620.

The expected value if 10,000 lottery tickets are sold will be:

= 10000 × [(2 × 45379620- 1)/45379620] - (1/45379620) × 1000000

= $19780

Therefore, the expected value is $19780.

Learn more about probability on:

https://brainly.com/question/24756209

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