Answer:
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
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