Question

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.

Explain your work please.

Answer #1

**ANSWER::**

**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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The odds of winning a certain lottery with a single ticket is 1
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bought.
1. Please assume the tickets win or lose independently of each
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during the two months.
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approximation is a good one.

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