Probability and Combinations in Lotteries

This video tutorial explains the probability of winning a state lottery by selecting 6 different numbers from 1 to 44. It covers the use of combinations to calculate the probability of winning with one ticket and with 2,000 tickets. The tutorial demonstrates the calculation process both manually and using a calculator, and expresses the probability as a fraction, decimal, and percentage. The video highlights the very low probability of winning the lottery, even with multiple tickets.

In a state lottery, how many different numbers does a player choose from?

• 6

• 50

• 44

• 10

What is the formula for calculating combinations?

• N choose R = R! / N!

• N choose R = N! / (N-R)! R!

• N choose R = N! / R!

• N choose R = (N-R)! / N!

What is the total number of ways to choose 6 numbers from 44?

• 7,059,052

• 1,764,763

• 6

• 44

How is the probability of winning with one ticket expressed as a fraction?

• 1/1,764,763

• 1/6

• 1/44

• 1/7,059,052

What is the probability of winning with one ticket expressed as a percentage?

• 0.1417%

• 0.01417%

• 0.001417%

• 0.00001417%

What is the probability of winning with one ticket expressed as a decimal?

• 0.001417

• 0.0001417

• 0.00001417

• 0.0000001417

How many favorable ways are there to win with 2,000 tickets?

• 2,000

• 1

• 7,059,052

• 44

What is the simplified fraction for the probability of winning with 2,000 tickets?

• 500/1,764,763

• 2,000/44

• 1/44

• 1/7,059,052

What is the probability of winning with 2,000 tickets expressed as a percentage?

• 28.33%

• 0.2833%

• 0.02833%

• 2.833%

What is the probability of winning with 2,000 tickets expressed as a decimal?

• 0.0002833

• 0.002833

• 0.2833

• 0.02833