In Lotto 649, you must select 6 numbers from 1-49. The probability that you will match 3 numbers is? using hypergeometric distribution
To calculate the probability of matching exactly 3 numbers in Lotto 649, we can use the hypergeometric distribution formula:
P(X = k) = (C(k, K) * C(n - k, N - K)) / C(n, N)
Where:
- P(X = k) is the probability of matching exactly k numbers
- C(n, N) is the number of ways to choose N items from a total of n items
- n is the total number of items in the population (49 numbers in Lotto 649)
- N is the total number of items to be chosen (6 numbers in Lotto 649)
- k is the number of "successes" in the population (3 numbers matched)
- K is the number of "successes" to be chosen (3 numbers to match)
Plugging in the values, we get:
P(X = 3) = (C(3, 6) * C(46, 3)) / C(49, 6)
P(X = 3) = (20 * 15,596) / 13,983,816
P(X = 3) = 311,920 / 13,983,816
P(X = 3) ≈ 0.0223
Therefore, the probability of matching exactly 3 numbers in Lotto 649 is approximately 0.0223, or 2.23%.