In a lottery, a player selects six numbers between 1 and 36 inclusive. The six winning numbers (all different) areselected at random from the numbers 1-36. To win a prize, the player must match three or more of the winningnumbers. What is the probability that the player matches exactly 3 numbers?
A) 0.0417
B) 0.0347
C) 0.0486
D) 0.0521

Question

Quizplus · Accepted Answer

The probability of matching exactly 3 numbers is 0.0417. This can be calculated using the hypergeometric distribution, which is a probability distribution that describes the number of successes in a sequence of n independent experiments, each of which has a constant probability of success. In this case, the number of successes is the number of winning numbers that the player matches, and the number of experiments is the number of numbers that the player selects. The probability of matching exactly 3 numbers is given by the following formula:```P(X = 3) = (C(6, 3) * C(30, 3)) / C(36, 6)```where:* C(n, k) is the binomial coefficient, which represents the number of ways to choose k elements from a set of n elements.* X is the number of winning numbers that the player matches.Plugging in the values, we get:```P(X = 3) = (C(6, 3) * C(30, 3)) / C(36, 6) = 0.0417```

In a Lottery, a Player Selects Six Numbers Between 1