In Lotto 649, you must select 6 numbers from 1-49. The probability that you will match 2 or less numbers is? using hypergeometric distribution
To find the probability of matching 2 or less numbers in Lotto 649, we can use the hypergeometric distribution formula:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
Where:
- P(X = 0) = (Number of ways to choose 0 matching numbers * Number of ways to choose the remaining 6 numbers) / Total number of ways to choose 6 numbers from 49
- P(X = 1) = (Number of ways to choose 1 matching number * Number of ways to choose the remaining 5 numbers) / Total number of ways to choose 6 numbers from 49
- P(X = 2) = (Number of ways to choose 2 matching numbers * Number of ways to choose the remaining 4 numbers) / Total number of ways to choose 6 numbers from 49
We can calculate these probabilities as follows:
P(X = 0) = (C(6, 0) * C(43, 6)) / C(49, 6) = (1 * 6,096,454) / 13,983,816 ≈ 0.4351
P(X = 1) = (C(6, 1) * C(43, 5)) / C(49, 6) = (6 * 7,001,304) / 13,983,816 ≈ 0.3363
P(X = 2) = (C(6, 2) * C(43, 4)) / C(49, 6) = (15 * 1,086,006) / 13,983,816 ≈ 0.2003
Therefore, P(X ≤ 2) = 0.4351 + 0.3363 + 0.2003 = 0.9717
So, the probability that you will match 2 or less numbers in Lotto 649 is approximately 0.9717 or 97.17%.