A box contains 3 red marbles, 5 white marbles and 7 blue marbles, 2 balls are drawn at random. Calculate probability? a, There is 1 red ball out of the 2 balls drawn b, There is at least 1 red ball out of 2 balls drawn

a) 0.3429 = 34.29% probability there is 1 red ball out of the 2 balls drawn.

b) 0.3715 = 37.15% probability that there is at least 1 red ball out of 2 balls drawn

Step-by-step explanation:

The balls are drawn without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

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

In which:

x is the number of successes.

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:

3 + 5 + 7 = 15 balls, which means that

3 red, which means that

2 drawn, which means that

a) Probability there is 1 red ball out of the 2 balls drawn

This is

So

0.3429 = 34.29% probability there is 1 red ball out of the 2 balls drawn.

b) Probability there is at least 1 red ball out of 2 balls drawn

This is:

So

0.3715 = 37.15% probability that there is at least 1 red ball out of 2 balls drawn

75

step-by-step explanation: