Question

In a certain lottery, 50 balls numbered 1 through 50 are placed in a machine and five of them are drawn at random. If the five numbers drawn the numbers that a player had chosen , the player wins $1000000.

a) If in this lottery, the order the numbers are drawn in does not matter, compute the probability that you win the million-dollar prize if you purchase a single lottery ticket.

Answer 1

To calculate the probability of winning the million-dollar prize in this lottery, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Step-by-step explanation:

To calculate the probability of winning the million-dollar prize in this lottery, we need to determine the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes is the number of ways to choose 5 balls out of 50, which can be calculated using combinations: C(50, 5) = 2,118,760.

The number of favorable outcomes is 1, because there is only 1 way to choose the 5 numbers that the player had chosen.

Therefore, the probability of winning the million-dollar prize is 1 divided by the total number of possible outcomes: 1/2,118,760 ≈ 0.000000472 or 4.72 x 10^-7.