Question

Find the probability of winning a lottery with the following rule. Select the winning numbers from​ 1, 2, . . .​ ,34 . ​(In any order. No​ repeats.)

Answer 1

The probability of winning the lottery is approximately 10.05%.

Step-by-step explanation:

To find the probability of winning the lottery, we need to determine the number of possible winning combinations and divide it by the total number of possible combinations.

In this case, the winning numbers can be selected from 1 to 34 without repeats. Since the order doesn't matter, we can use the combination formula.

The number of possible winning combinations is C(34, 5) = 34! / (5!(34-5)!), which can be calculated as 278,256.

The total number of possible combinations is C(34, 5), which equals 34! / (5!(34-5)!), resulting in 2,760,681.

Therefore, the probability of winning the lottery is 278,256 / 2,760,681, which simplifies to approximately 0.1005 or 10.05%.

Answer 2

Complete Question

Find the probability of winning a lottery with the following rule. Select the six winning numbers from​ 1, 2, . . .​ ,34 . ​(In any order. No​ repeats.)

Answer:

The probability is
`P(winning ) = 7.435 *10^(-7)`

Step-by-step explanation:

From the question we are told that

The total winning numbers n = 34

The total number to select is r = 6

The total outcome of lottery is mathematically represented as

`t_(outcome)) = \left n } \atop {}} \right. C_r`

`t_(outcome)) = (n! )/((n-r )! r!)`

substituting values

`t_(outcome)) = ( 34 ! )/((34 - 6 )! 6!)`

`t_(outcome)) = ( 34 ! )/(28 ! 6!)`

`t_(outcome)) =1344904`

The number of desired outcome is

`t_(desired) = 1`

this is because the desired outcome is choosing the six winning number

The probability of winning a lottery is mathematically represented as

`P(winning ) = (t_(desired))/(t_(outcome))`

substituting values

`P(winning ) = (1)/(1344904 )`

`P(winning ) = 7.435 *10^(-7)`