Approximate the probability of a chance event - HiSET

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Question

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

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.

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Question

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?

Answer

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

The probability of a green marble is $\dfrac {5}{40}$ .

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 $\dfrac {15}{39}$ .

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, $\dfrac {5}{40}\times \dfrac {15}{39}=\dfrac {5\times 15}{40\times 39}=\dfrac {75}{1560}$

Step 4: Simplify...

$\dfrac {75}{1560}=\dfrac {\dfrac {75}{5}}{\dfrac {1560}{5}}=\dfrac {15}{312}=\dfrac {15/3}{312/3}=\dfrac {5}{104}$

$\dfrac {5}{104}$ is the answer.

Compare your answer with the correct one above

Question

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

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.

Compare your answer with the correct one above

Question

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?

Answer

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

The probability of a green marble is $\dfrac {5}{40}$ .

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 $\dfrac {15}{39}$ .

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, $\dfrac {5}{40}\times \dfrac {15}{39}=\dfrac {5\times 15}{40\times 39}=\dfrac {75}{1560}$

Step 4: Simplify...

$\dfrac {75}{1560}=\dfrac {\dfrac {75}{5}}{\dfrac {1560}{5}}=\dfrac {15}{312}=\dfrac {15/3}{312/3}=\dfrac {5}{104}$

$\dfrac {5}{104}$ is the answer.

Compare your answer with the correct one above

Question

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

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.

Compare your answer with the correct one above

Question

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?

Answer

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

The probability of a green marble is $\dfrac {5}{40}$ .

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 $\dfrac {15}{39}$ .

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, $\dfrac {5}{40}\times \dfrac {15}{39}=\dfrac {5\times 15}{40\times 39}=\dfrac {75}{1560}$

Step 4: Simplify...

$\dfrac {75}{1560}=\dfrac {\dfrac {75}{5}}{\dfrac {1560}{5}}=\dfrac {15}{312}=\dfrac {15/3}{312/3}=\dfrac {5}{104}$

$\dfrac {5}{104}$ is the answer.

Compare your answer with the correct one above

Question

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

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.

Compare your answer with the correct one above

Question

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?

Answer

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

The probability of a green marble is $\dfrac {5}{40}$ .

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 $\dfrac {15}{39}$ .

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, $\dfrac {5}{40}\times \dfrac {15}{39}=\dfrac {5\times 15}{40\times 39}=\dfrac {75}{1560}$

Step 4: Simplify...

$\dfrac {75}{1560}=\dfrac {\dfrac {75}{5}}{\dfrac {1560}{5}}=\dfrac {15}{312}=\dfrac {15/3}{312/3}=\dfrac {5}{104}$

$\dfrac {5}{104}$ is the answer.

Compare your answer with the correct one above

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