Question

in the lottery the player has to guess correctly r numbers that are drawn out of n numbers. the probability, p, of guessing m numbers out of the r numbers can be calculated by the expression: where cxy

Answer 1

In the lottery game, the probability of guessing a specific number of numbers correctly can be calculated using a combination formula.

Step-by-step explanation:

In the lottery game, where the player has to guess correctly r numbers out of n numbers, the probability of guessing m numbers out of the r numbers can be calculated using the expression:

P(m) = (c(m, r) * c(n-m, r-m)) / c(n, r)

where c(x, y) represents the combination of selecting y items from a set of x items.

For example, if the player has to guess 3 numbers (r) out of 10 numbers (n), and wants to calculate the probability of guessing exactly 2 numbers (m), the expression would be:

P(2) = (c(2, 3) * c(8, 1)) / c(10, 3)