To calculate the probability of having exactly 5 common numbers in two Mark Six draws, we need to consider the combinations and probabilities involved. Here’s a step-by-step approach:
Total Combinations for One Draw: In Mark Six, 6 numbers are drawn from a pool of 49. The number of possible combinations is given by:
(649)=6!(49−6)!49!=13,983,816
Combinations for 5 Common Numbers: To have exactly 5 common numbers in two draws, we need to select 5 numbers from the 6 drawn in the first draw and 1 number from the remaining 43 numbers (49 - 6 = 43). The number of ways to choose 5 out of 6 is:
(56)=6
The number of ways to choose 1 out of the remaining 43 is:
(143)=43
Total Favorable Combinations: The total number of favorable combinations for having exactly 5 common numbers in two draws is:
6×43=258
Probability Calculation: The probability of having exactly 5 common numbers in two draws is the ratio of the number of favorable combinations to the total number of combinations:
P(5 common numbers)=13,983,816258≈0.00001845
So, the probability of having exactly 5 common numbers in two Mark Six draws is approximately 0.00001845, or about 0.001845%.
P.Plate2024-09-20 05:05:42
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To calculate the probability of having exactly 5 common numbers in two Mark Six draws, we need to consider the combinations and probabilities involved. Here’s a step-by-step approach:
Total Combinations for One Draw: In Mark Six, 6 numbers are drawn from a pool of 49. The number of possible combinations is given by:
(49C6)=6!(49−6)!49!=13,983,816
Combinations for 5 Common Numbers: To have exactly 5 common numbers in two draws, we need to select 5 numbers from the 6 drawn in the first draw and 1 number from the remaining 43 numbers (49 - 6 = 43). The number of ways to choose 5 out of 6 is:
(6C5)=6
The number of ways to choose 1 out of the remaining 43 is:
(43C1)=43
Total Favorable Combinations: The total number of favorable combinations for having exactly 5 common numbers in two draws is:
6×43=258
Probability Calculation: The probability of having exactly 5 common numbers in two draws is the ratio of the number of favorable combinations to the total number of combinations:
P(5 common numbers)=13,983,816258≈0.00001845
So, the probability of having exactly 5 common numbers in two Mark Six draws is approximately 0.00001845, or about 0.001845%.