Question

The odds of winning a certain lottery with a single ticket is 1 in 300,000,000. In...

The odds of winning a certain lottery with a single ticket is 1 in 300,000,000. In May and June, 200,000,000 tickets were bought.

1. Please assume the tickets win or lose independently of each other and give the exact probability that there was no winner during the two months.

2. Only using a basic scientific calculator, give an approximation to the same question from part 1. Explain why this approximation is a good one.

Given odds of winning a certain lottery with a single ticket is 1 in 300,000,000

So the probability of winning the lottery = 1 / (1 + 300000000)

= 1/300000001

= 0.0000000033

Question (1):

The Probability of winning during the two months = 200,000,000 * Probabilty of winning the lottery by single ticket

=  200,000,000 * 0.0000000033

= 0.666666664444444

So Probabality that there was no winner during the two months = 1 - 0.666666664444444

= 0.3333333355555556

Question (2):

The probability that there was no winner during the two months.from the scientific calculator is 0.333333336

The approximation is good because the value is same for Question 1 and Question 2 upto 8 decimals

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