To win the jackpot in a lottery in Iowa, participants have to select 6 unique winning numbers out of the numbers 1 through 49 in which the order does not matter. What is the probability of winning the jackpot? State your answer as both a fraction and decimal to at least 10 decimal places. In light of your answer, briefly comment on why one comedian commented several years ago that, "your odds of winning the lottery are about as good if you don't play than game at all than if you do."

Question

To win the jackpot in a lottery in Iowa, participants have to select 6 unique winning numbers out of the numbers 1 through 49 in which the order does not matter. What is the probability of winning the jackpot? State your answer as both a fraction and decimal to at least 10 decimal places. In light of your answer, briefly comment on why one comedian commented several years ago that, "your odds of winning the lottery are about as good if you don't play than game at all than if you do."

Answer 1

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

Assuming that the numbers cannot be repeated,

6/49 * 5/48 * 4/47 * 3/46 * 2/ 45 * 1/44 = ?

Answer 2

.0000000715

Answer 3

To calculate the probability of winning the jackpot in the Iowa lottery, we need to determine the number of possible combinations of 6 unique winning numbers out of the numbers 1 through 49, and then divide it by the total number of possible combinations.

First, let's calculate the number of possible combinations. We use the combination formula, which is:

nCr = n! / (r!(n-r)!)

In this case, n is the total number of available numbers (49), and r is the number of numbers we want to select (6). We can substitute these values into the formula:

49C6 = 49! / (6!(49-6)!)

Now, let's calculate this value:

49C6 = (49 * 48 * 47 * 46 * 45 * 44) / (6 * 5 * 4 * 3 * 2 * 1)
= 13,983,816

So, there are a total of 13,983,816 possible combinations of 6 unique winning numbers out of the numbers 1 through 49.

To calculate the probability, we need to divide the number of desired outcomes (winning combinations) by the total number of possible outcomes. In this case, there is only one winning combination.

Probability = 1 / 13,983,816

Now, let's express this fraction as a decimal. Dividing 1 by 13,983,816 gives us approximately 0.0000000715112383.

So, the probability of winning the jackpot is approximately 1 in 13,983,816 or 0.0000000715112383.

Regarding the comedian's comment, the reason they mentioned that the odds of winning the lottery are about the same whether you play or not is because the probability of winning is extremely low. The odds of winning the jackpot are so minuscule that the difference between playing and not playing makes a negligible impact on your chances of winning. Hence, the comedian humorously highlights the futility of the endeavor.