Question

The Super Lotto Plus game consists of a player selecting five different numbers from 1 to 47 and a mega number from 1 to 27 (the order is unimportant and the mega number need not be different from the other numbers). (11) What is the probability of all five numbers and the mega number matching the winning numbers

Answer 1

1/41416353 probability of all five numbers and the mega number matching the winning numbers

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the order of the numbers is not important. So we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

Probability of the five numbers matching:

Desired outcomes: 1 -> the matching numbers

Total outcomes: 5 from a set of 47. So

`T = C_(47,5) = (47!)/(5!(47-5)!) = 1533939`

Probability:

`p_(S) = (1)/(1533939)`

Probability of the mega number matching:

1 from a set of 27. So

`p_M = (1)/(27)`

Probability of both matching:

Independent events, so we multiply the probabilities:

`p = p_S*p_M = (1)/(1533939)*(1)/(27) = (1)/(41416353)`

1/41416353 probability of all five numbers and the mega number matching the winning numbers