On a particular game show, there are 8 covered buckets and 2 of them contain a ball. To win the game, a contestant must select both buckets that contain a ball. Find the
probability that a contestant wins the game if he/she gets to select 4 of the buckets.

0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.

Step-by-step explanation:

The buckets are chosen without replacement, which means that the hypergeometric distribution is used 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:

8 covered buckets, so N = 8.

4 buckets are selected, so n = 4.

2 contain a ball, which means that k = 2.

Find the probability that a contestant wins the game if he/she gets to select 4 of the buckets.

This is P(X = 2). So

0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.

hope it

step-by-step explanation:

x^(1/6) · x^(1/6) · x^(1/6)   ·x^(1/6) = x^(4/6)   since we add the exponents

4/6 can be simplified to 2/3

the simplified form is x^(2/3)