Question

Suppose that in a lottery game you are to pick five different integers between 1 and 50, including 1 and 50, and a sixth integer between 1 and 40, including 1 and 40. a) What is the probability that you win the jackpot where the first five numbers that you picked match the five numbers drawn and the sixth number you pick matches the sixth number drawn

Answer 1

Answer:

The probability of wining the jackpot = 1.180×10⁻⁸

Step-by-step explanation:

The number of possible ways to pick first 5 different integers between 1 and 50 is given by

n₁ = ⁵⁰C₅

n₁ = 2118760

The number of possible ways to pick 6th integer between 1 and 40 is given by

n₂ = ⁴⁰C₁

n₂ = 40

The number of ways to correctly guess the first five integers is given by

p₁ = ⁵C₅

p₁ = 1

The number of ways to correctly guess the 6th integer is given by

p₂ = ¹C₁

p₂ = 1

The probability of wining the jackpot where the first five numbers picked match the five numbers drawn and the sixth number picked matches the sixth number drawn is given by

$P = \frac{p_{1} \cdot p_{1}} {n_{1} \cdot n_{2}}\\P = \frac{1 \cdot 1}{2118760 \cdot 40}\\P = \frac{1}{84750400}\\P = 1.180 \times 10^{-8}$

Therefore, the probability of wining the jackpot is 1.180×10⁻⁸