in a particular state\'s lottery, you pick 5 different numbers (white balls) bet

Question

in a particular state's lottery, you pick 5 different numbers (white balls) between 1 and 48, and a another ball (yellow ball) between 1 and 18 for each $2.00 Play. once a ball is picked, it does not go back in the bin and the order does not matter. I must show work. a. What is the probability of winning the big jackpot by picking all the numbers both white and Yellow b. what is the probability of winning by picking 0 white balls and not the yellow one (getting none of the numbers) c. what is the probability of winning by picking 3 out of 5 white balls and the yellow one. d. how much is the expected return of winning a $150.00 prize in part c?

Explanation / Answer

A) Number of ways of chosing winning combination = 5C5 = 1

Number of ways in which winning 5 numbers can be chosen from 48 white balls = 48C5

Number of ways in which the winning yellow ball can be chosen = 18C1 = 18

Probability of winning = number of ways of chosing winning combination/(total number of options available)

P(winning the big jackpot) = 1/(48C5 x 18C1)

= 3.244x10-8

B) number of ways of chosing 5 white balls from the white balls other than the 5 = (48-5)C5

= 43C5

Number of ways of chosing any other yellow ball = 17

P(winning by chosing 0 white balls and not the one yellow) = (43C5)x17/(48C5x18)

= 0.5309

C) Number of ways of picking 3 out of 5 white balls = (3 white of 5 winning) x (2 white out of other whote balls)

= 5C3 x 43C2

Number of ways of chosing yellow = 1

So, P(winning by chosing 2 out of 5 white and 1 yellow) = 5C3x43C2x1/(48C5x18)

= 0.0003

Expected return = 150x0.0003 - cost of ticket

= -$1.955

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