Compound Probability

Front

What is compound probability?

Back

Compound probability refers to the probability of two or more events happening at the same time or in sequence. It can be calculated using the multiplication rule for independent events or the addition rule for mutually exclusive events.

Front

How do you calculate the probability of independent events occurring in sequence?

Back

To calculate the probability of independent events occurring in sequence, multiply the probabilities of each individual event. For example, P(A and B) = P(A) * P(B).

Front

What is the formula for calculating the probability of drawing two marbles without replacement?

Back

The probability of drawing two marbles without replacement is calculated as P(A) * P(B|A), where P(B|A) is the probability of drawing the second marble given that the first marble has already been drawn.

Front

If a bag contains 4 blue marbles and 3 red marbles, what is the probability of picking a blue marble and then a red marble with replacement?

Back

The probability is P(blue) * P(red) = (4/7) * (3/7) = 12/49.

Front

What is the total number of outcomes when tossing a coin and rolling a die?

Back

The total number of outcomes is the product of the number of outcomes for each event: 2 (coin) * 6 (die) = 12.

Front

How do you find the probability of drawing a specific color marble from a bag?

Back

To find the probability of drawing a specific color marble, divide the number of marbles of that color by the total number of marbles in the bag.

Front

What is the probability of drawing a purple marble second if the first drawn marble is blue and not replaced?

Back

If the first marble is blue, the probability of drawing a purple marble second is 3 purple marbles remaining out of 4 total marbles left, so P(purple) = 3/4.

Front

What is the probability of rolling a 2 followed by a 5 on two six-sided dice?

Back

The probability is P(2) * P(5) = (1/6) * (1/6) = 1/36.

Front

What is the multiplication rule in probability?

Back

The multiplication rule states that the probability of the occurrence of two independent events is the product of their individual probabilities.

Front

What is the addition rule in probability?

Back

The addition rule states that the probability of the occurrence of at least one of two mutually exclusive events is the sum of their individual probabilities.