What is the probability of winning the jackpot in Lotto 6-49? (Matching all 6 correct number.
P(winning lotto 6-49)= [(6/6)(43/0)] / (49/6)
= 1/13,983,816
= 7.15 x 10 *-08
Is this correct?
Then how would I do this?
A new lottery rule of winning Lotto 6-49 is when all of your numbers match or 5 of your numbers match. Find the probability that you win the lottery.
To find the probability of winning the jackpot in Lotto 6-49, you need to consider the total number of possible outcomes and the number of favorable outcomes.
In Lotto 6-49, you choose 6 numbers from a pool of 49 possible numbers. The order of the numbers does not matter for this calculation.
The total number of possible outcomes is given by the combination formula:
N = C(49, 6) = 49! / (6! * (49 - 6)!)
In this formula, "C(n, r)" represents the number of combinations of "n" items taken "r" at a time, and "!" denotes the factorial function.
The probability P of winning the jackpot, where all 6 numbers match, is given by:
P(winning jackpot) = 1 / N
Substituting the values into the formula, you would have:
P(winning jackpot) = 1 / C(49, 6) = 1 / (49! / (6! * 43!))
Simplifying further, you would calculate:
P(winning jackpot) = (6! * 43!) / 49!
For the given problem, the calculation in the provided expression seems incorrect. The correct calculation should be:
P(winning jackpot) = (6/6) * (43/0) * (42/0) * (41/0) * (40/0) * (39/0) / (49/6) = 1 / (49! / (6! * 43!)) ≈ 1 / 13,983,816
So, the probability of winning the jackpot in Lotto 6-49, where all 6 numbers match, is approximately 1 in 13,983,816.
Now, for the second part of your question, where the new rule states that you can also win the lottery if 5 of your numbers match, you need to calculate the probability of winning in this scenario.
To do this, you would need to calculate the probability of getting exactly 5 out of 6 numbers correct.
The number of combinations of choosing 5 numbers correctly out of 6 is C(6, 5) = 6.
Therefore, the probability of winning with 5 out of 6 numbers is 6 times higher than winning with all 6 numbers. So, the probability of winning the lottery with either all 6 correct numbers or 5 correct numbers would be:
P(winning lottery) = P(winning jackpot) + 6 * P(5 out of 6 correct)
You can now substitute the values for P(winning jackpot) that you calculated earlier and calculate the value of P(5 out of 6 correct) using the same combination formula process.
I hope this explanation helps you understand how to calculate the probabilities for winning the lottery in various scenarios.