In the Virginia instant lottery there are ten different 5 Sc

In the Virginia instant lottery, there are ten different $5 Scratcher games. Your favorite, “Hit the Jackpot,” is advertised to have a 1 in 4.37 chance of winning, and a 1 in 664,457 chance of hitting the top prize of $200,000. Seven of the seven top prizes are still available.

a: If you buy five of these tickets and outcomes are independent, the probability of winning at least once in these five draws is?

b: If you buy five of these tickets and outcomes are independent, the probability that you lose all five times is

c: If you buy five of these tickets and outcomes are independent, the probability that you win all five times is?

d: If you buy five of these tickets and outcomes are independent, the probability that you will NOT win the jackpot is?

Solution

a)

Here,

P(win) = 1/4.37 = 0.228832952

P(win at least once) = 1 - P(all losses)

= 1 - (1-0.228832952)^5

= 0.727264093 [ANSWER]

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b)

P(all losses) = (1-0.228832952)^5 = 0.272735907 [ANSWER]

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c)

P(win all five) = 0.228832952^5 = 0.00062747 [ANSWER]

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d)

Here,

P(not win jackpot) = 1 - 1/664457 = 0.999998495

Thus,

P(all 5 doesn\'t win) = 0.999998495^5 = 0.999992475 [ANSWER]