Approximate the probability of a chance event - HiSET

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...

is the answer.

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.

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...

is the answer.

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.

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...

is the answer.

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.

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...

is the answer.