Which Probability Formula should I Use

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What is the formula for calculating the probability of drawing a specific color of marble from a bag?

Back

The probability of drawing a specific color is given by the formula: P(color) = \frac{number\ of\ desired\ color\ marbles}{total\ number\ of\ marbles}.

Front

How do you calculate the probability of drawing multiple marbles of different colors with replacement?

Back

When drawing with replacement, the probability is calculated by multiplying the individual probabilities: P = P(color1) \cdot P(color2) \cdot P(color3) \cdots.

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What is the difference between drawing with replacement and without replacement?

Back

With replacement means the marble is put back into the bag after drawing, keeping the total number constant. Without replacement means the marble is not returned, reducing the total number of marbles for subsequent draws.

Front

How do you calculate the probability of drawing at least one specific color?

Back

To find the probability of drawing at least one specific color, use the complement rule: P(at least one) = 1 - P(none).

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What is the formula for combinations, and when is it used in probability?

Back

The formula for combinations is C(n, k) = \frac{n!}{k!(n-k)!}. It is used when the order of selection does not matter.

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How do you calculate the probability of drawing a specific sequence of colors?

Back

To calculate the probability of a specific sequence, multiply the probabilities of each individual draw: P(sequence) = P(color1) \cdot P(color2) \cdot P(color3) \cdots.

Front

What is the probability of drawing a boy and then a girl from a group of boys and girls?

Back

The probability is calculated as: P(boy) \cdot P(girl|boy) = \frac{number\ of\ boys}{total} \cdot \frac{number\ of\ girls}{total - 1}.

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How do you calculate the probability of drawing all girls from a group?

Back

The probability of drawing all girls is calculated by multiplying the probabilities of each draw: P(all\ girls) = P(girl1) \cdot P(girl2|girl1) \cdot P(girl3|girl1, girl2).

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What is the formula for calculating the probability of drawing at least 3 yellow marbles?

Back

To calculate the probability of drawing at least 3 yellow marbles, sum the probabilities of drawing 3 yellow and 1 non-yellow, and 4 yellow: P(at\ least\ 3\ yellow) = P(3\ yellow) + P(4\ yellow).

Front

How do you calculate the probability of drawing a specific combination of colors?

Back

Use the combination formula to find the number of ways to choose the colors, then divide by the total combinations: P(specific\ combination) = \frac{C(desired\ colors)}{C(total\ colors)}.