In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1 through 45) and matching the number on the gold ball (1 through 32). If one ticket is purchased, what is the probability of winning the jackpot?
There are a total of 45 white balls and the player must match all 5 of them.
The probability of matching the first number drawn is 1 out of 45.
The probability of matching the second number drawn is 1 out of 44 (since one number has already been drawn).
The probability of matching the third number drawn is 1 out of 43.
The probability of matching the fourth number drawn is 1 out of 42.
The probability of matching the fifth number drawn is 1 out of 41.
Since the order doesn't matter, we need to multiply these probabilities by the number of possible permutations of the 5 numbers, which is 5! (5 factorial).
So, the probability of matching all 5 white balls in any order is:
(1/45) * (1/44) * (1/43) * (1/42) * (1/41) * 5! = (1/45) * (1/44) * (1/43) * (1/42) * (1/41) * 120 = 1/8,145,060
There are also 32 possible outcomes for the gold ball and the player must match it.
The probability of matching the gold ball is 1 out of 32.
Therefore, the probability of winning the jackpot is:
(1/8,145,060) * (1/32) ≈ 0.0000001544 or about 0.00001544%.
So, the probability of winning the jackpot with one ticket is approximately 0.00001544%.