Question

The chances of winning the Powerball lottery jackpot with a single ticket is 1 in 292,201,338. For the purposes of this problem, assume it is 1 in 300,000,000.

During February and March, 210,073,226 Powerball tickets were sold. For the purposes of this problem, assume 200,000,000 were sold.

a.)Assuming the tickets win or lose independently of one another, give the exact probability that there was no jackpot winner during these two months.

b.)Using a basic scientific calculator, give an approximation to your answer in part (a). You must justify why your approximation is close to the exact answer.

Answer 1

ANSWER::

a).

x = no. of winner

p = P(win) = 1 / 300,000,000

n = 200,000,000

P(0) = 200,000,000C0 * (p^0) * (1 - p)^(200,000,000 - 0)

= 0.51273301126

b).

P(win) = 1 in 300,000,000

= 1 / 300,000,000

P(not win) = 1 - P(win)

= 1 - 1 / 300,000,000

= 0.99999999666

= 0.999999997 {approximation}

P(no winner) = P(not win)^(tickets sold)

= (0.999999997)^(200000000)

= 0.5488

it is close as we have just rounded the value of p(win)

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