In Lotto 649, find the probability that:
a) You have all six correct numbers.
b) You have three correct numbers.
To find the probability of winning in Lotto 649, we need to understand the rules of the game. In Lotto 649, players choose six numbers from a range of 1 to 49. The winning numbers are drawn randomly, and the goal is to match as many numbers as possible.
a) Probability of having all six correct numbers in Lotto 649:
There is only one possible combination of six numbers that will result in a win - the winning combination itself. Therefore, the probability of selecting the exact combination of six numbers drawn is 1 out of the total number of possible combinations.
To calculate the total number of possible combinations, we need to use the concept of combinations. In this case, we have 49 numbers to choose from, and we want to select six numbers. The formula for combinations is nCr, which represents the number of ways to choose r objects from a set of n objects.
Thus, the total number of possible combinations for Lotto 649 is calculated as:
49C6 = (49!)/(6!(49-6)!) = 13,983,816
Therefore, the probability of having all six correct numbers in Lotto 649 is 1 in 13,983,816.
b) Probability of having three correct numbers in Lotto 649:
To determine the probability of having three correct numbers, we need to select three out of the six winning numbers and three out of the remaining 43 non-winning numbers. The order does not matter in this case, so we will use combinations to calculate the probability.
The number of ways to select three winning numbers out of six is calculated as:
6C3 = (6!)/(3!(6-3)!) = 20
The number of ways to select three non-winning numbers out of the remaining 43 is calculated as:
43C3 = (43!)/(3!(43-3)!) = 22,545
To find the total number of combinations with three correct numbers, we multiply these two values together:
20 * 22,545 = 450,900
Therefore, the probability of having three correct numbers in Lotto 649 is 1 in 450,900.