Find the probabiity of winning a lottery with the following. Select the six winning number from 1, 2, ..., 42. (In any order. No repeats.)P(winning) = (Type an integer or a simplified fraction.)
Question
Find the probabiity of winning a lottery with the following. Select the six winning number from 1, 2, ..., 42. (In any order. No repeats.)P(winning) = (Type an integer or a simplified fraction.)
Solution
The probability of winning a lottery can be calculated using the concept of combinations in probability.
In this case, we are selecting 6 numbers out of 42. The order of selection does not matter and there are no repeats.
The total number of ways to select 6 numbers out of 42 is given by the combination formula:
C(n, r) = n! / [r!(n-r)!]
where:
- n is the total number of options (42 in this case),
- r is the number of selections to be made (6 in this case),
- "!" denotes factorial, which is the product of all positive integers up to that number.
So, the total number of combinations is:
C(42, 6) = 42! / [6!(42-6)!]
The probability of winning is the ratio of the successful outcomes to the total outcomes. Since there is only one successful outcome (selecting the winning numbers), the probability of winning is:
P(winning) = 1 / C(42, 6)
So, the probability of winning the lottery is 1 divided by the total number of ways to select 6 numbers out of 42.
Similar Questions
In a certain state's lottery, 40 balls numbered 1 through 40 are placed in a machine and eight of them are drawn at random. If the eight numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. In this lottery, the order the numbers are drawn in does not matter.Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket. Write your answer as a reduced fraction.
In the above scenario, when there were 53 numbers to choose from, and players pick 6 numbers, the total number of combinations was 22,957,480. The calculations for this are shown step by step in the above image using the Combination formula. Use the information above to answer the following questions: 1. What are the odds of winning in this scenario with one winning ticket? 2. What would the odds of winning be if there are 54 numbers instead of 53 with one winning ticket?3. Suppose the Lottery Commission offers a Pick 5 game, where the players choose 5 out of 40 numbers. What would the odds of winning be if there are three winning tickets in this drawing?
A lottery contains eight prizes and twenty blanks. If a lottery is randomly drawn, then what is the probability of getting a prize?1/82/52/71/5
A die is rolled 600 times and the occurrence of the outcomes 1, 2, 3, 4, 5 and 6 are given below in the table: Outcome 1 2 3 4 5 6 Frequency 200 30 120 100 50 100 If one of the dice rolls is picked at random, find the probability of getting a prime number.A)
If the probability of winning a division 4 lotto prize (4 winning numbers) is , what is the probability of not winning a division 4 lotto prize?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.