Question

A certain lottery consists of selecting five different numbered balls from numbered 1 to 16 white balls and one from 1 to 13 gold Mega balls. A player wins the jackpot by matching all five numbers drawn from white balls​ (1 through 16​) and matching the number on the gold Mega Ball​ (1 through 13​). What is the probability of winning the​ jackpot?

Answer 1

The probability of winning the jackpot in the given lottery is 1/(C(16, 5) * 13).

Step-by-step explanation:

To find the probability of winning the jackpot in the given lottery, we need to consider the number of ways to choose the 5 white balls and the 1 gold Mega ball correctly, and then divide it by the total number of possible outcomes. There are 16 white balls and 13 gold Mega balls to choose from. The probability of choosing 5 white balls correctly is 1 out of C(16, 5), which represents the number of ways to choose 5 balls out of 16. Similarly, the probability of choosing the gold Mega ball correctly is 1 out of 13. Since these two events are independent, we can multiply the probabilities together. Therefore, the probability of winning the jackpot is 1/(C(16, 5) * 13).

Answer 2

The answer is 1/56784

Step-by-step explanation: First, we calculate the number of sets of 5 number in 1-16 = 16C5

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

Therefore

16C5 = 16!/(5!(16-5)!)

Remember that n! = n*(n-1)*(n-2)*(n-3).....*2*1

Thus 16! = 16x15x14x13x12x11x10x9x8x7x6x5x4x3x2x1 = 20,922,789,888,000

(16-5)! = 11! = 11x10x9x8x7x6x5x4x3x2x1 = 39,916,800

5! = 5X4X3X2X1 = 120

Hence 16C5 = 20,922,789,888,000/(120x39,916,800)

= 4368

Number of winning sets of 5 numbers = 1

So P(Pick the proper set of 5 numbers) = 1/4368

P(Correct number of Gold Mega Balls) = 1/13

P(Winning the jackpot) = P(Pick the proper set of 5 numbers from white balls) and P(Pick Correct number of Gold Mega Ball)

Thus P(Winning the jackpot) = 1/4368 x 1/13 = 1/56784