In a lottery game, a player picks 7 numbers from 1 to 53. If 6 of the 7 numbers match those drawn, the player wins second prize. What is the probability of winning this prize?

0.000002089 probability of winning this prize

Step-by-step explanation:

After a number is chosen, it cannot be chosen again. So we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

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

In this question:

53 numbers, then N = 53.

7 numbers picked, so n = 7.

Total of desired outcomes(any number which the player picks is desired) is 7, so k = 7.

6 successes, so x = 6.

What is the probability of winning this prize?

0.000002089 probability of winning this prize

side xy = 10

sin(x) = 4/5

cos(x) = 3/5

tan(x) = 4/3

step-by-step explanation: