Question

Danielle purchased 6 raffle tickets for a school fundraiser. A number of n tickets are randomly drawn from a bag. The person with at least two winning tickets wins the grand prize. The function 6n³-6n²/8n³-12n²+4n models the probability of winning the grand prize. If 10 numbers are drawn (n = 10), what is the probability that Danielle will win the grand prize?

Answer 1

The probability that Danielle wins the grand prize when 10 numbers are drawn is approximately 0.7895 or 78.95%.

Step-by-step explanation:

The question involves calculating the probability that Danielle will win the grand prize given the function modeling the probability. With 10 numbers drawn (n = 10), we plug this into the function 6n³-6n²/8n³-12n²+4n to find the probability of winning the grand prize.

First, we substitute n = 10 into the equation:

P = (6*(10)³ - 6*(10)²) / (8*(10)³ - 12*(10)² + 4*10)

This simplifies to:

P = (6000 - 600) / (8000 - 1200 + 40)

Further simplification leads to:

P = 5400 / 6840

Now, by reducing the fraction, we get:

P = 5400/6840 = 0.7895

Therefore, the probability that Danielle wins the grand prize when 10 numbers are drawn is approximately 0.7895 or 78.95%.