# HiSET: Math : Approximate the probability of a chance event

## Example Questions

### Example Question #5 : Find Probabilities

If I have  quarters, what is the probability that I will get no more than  heads?

Explanation:

Step 1: If we have 3 quarters and each quarter has two outcomes, then there are  total outcomes that can come out of all of the rolls of the quarters.

Those rolls are:

HHH, HHT, HTH, THH, THT, TTH, TTT, HTT.

Step 2: Determine how many outcomes have no more than  heads....

We cannot count HHH because it has  heads.

We also cannot count TTT because it has no heads at all.

Step 3: We had  options and we can't take  options..so we have a total of  options left.

### Example Question #6 : Find Probabilities

In a sack, I have 20 red marbles, 15 blue marbles and 5 green marbles. What is the chance, without replacement, that I pick a green marble first and then pick a blue marble?

Explanation:

Step 1: Find the probability of getting a green marble...

The probability of a green marble is .

Step 2: Find the probability of getting a blue marble (without replacement)

When we have without replacement, we do not put the first marble we take out back into the sack. In this case, the total number of marbles in the sack is  less.

Probability of a blue marble is .

Step 3: To find the probability of both events happening at the same time, we need to multiply the probabilities in the first two steps.

So,

Step 4: Simplify...