In a lottery, the top cash prize was $684 million, going to three lucky winners. Players pick five different numbers from 1 to 52 and one number from 1 to 44. A player wins a minimum award of $300 by correctly matching threethree numbers drawn from the white balls (1 through 52) and matching the number on the gold ball (1 through 44). What is the probability of winning the minimum award?

Matching 3 white balls: There are 52 white balls, and you need to choose 3 of them. The order doesn't matter (you win regardless of which 3 are chosen).

Matching the gold ball: There are 44 gold balls, and you need to pick just 1 that matches the drawn number.

Favorable Outcomes:

White balls: The number of ways to choose 3 white balls out of 52 is:

Combinations (not permutations) because order doesn't matter.

We can use the combination formula: nCr = n! / (r! * (n-r)!)

In this case, n (total) = 52, r (chosen) = 3

Favorable outcomes (white) = 52! / (3! * (52-3)!) = 22,100

Gold ball: There are 44 possible winning outcomes for the gold ball (matching the drawn number).

Total Possible Outcomes:

There are two options for each of the 5 white balls and 44 options for the gold ball, resulting in a total of:

Total outcomes = 2 (choice for each white ball) * 2 (choice for each white ball) * ... (5 times) * 44 (gold ball)

Total outcomes = 2^5 * 44 = 11,264

Probability Calculation:

Since these events (matching white balls and matching the gold ball) are independent, we simply multiply the probabilities of each event to get the overall probability of winning the minimum award.

Probability = (Favorable outcomes for white balls) * (Favorable outcomes for gold ball) / Total possible outcomes

Probability = (22,100) * (44) / (11,264)

Probability ≈ 0.0085 (rounded to four decimal places)

Percentage:

Convert the probability to a percentage by multiplying by 100:

Probability ≈ 0.0085 * 100 ≈ 0.85%

Therefore, the probability of winning the minimum award in this lottery is approximately 0.85%.