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.

$ 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. $

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:

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

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:

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

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