Compound Probability

Front

What is compound probability?

Back

Compound probability refers to the probability of two or more events happening at the same time. 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?

Back

For independent events, the probability of both events occurring is the product of their individual probabilities. If A and B are independent, then P(A and B) = P(A) × P(B).

Front

What is the formula for calculating the probability of dependent events?

Back

For dependent events, the probability of both events occurring is calculated as P(A and B) = P(A) × P(B|A), where P(B|A) is the probability of B occurring given that A has occurred.

Front

If there are 3 red pens, 2 green pens, and 1 blue pen in a box, what is the total number of pens?

Back

The total number of pens is 3 + 2 + 1 = 6 pens.

Front

What is the probability of picking a red pen from the box?

Back

The probability of picking a red pen is P(red) = Number of red pens / Total number of pens = 3/6 = 1/2.

Front

What is the probability of picking a green pen after replacing a red pen?

Back

The probability of picking a green pen after replacing a red pen is P(green) = Number of green pens / Total number of pens = 2/6 = 1/3.

Front

How do you find the total number of combinations in a scenario with multiple choices?

Back

To find the total number of combinations, multiply the number of choices for each category. For example, if there are 6 flavors, 4 toppings, and 2 types of cones, the total combinations = 6 × 4 × 2 = 48.

Front

What is the probability of landing on blue first and then green on a spinner?

Back

If the spinner has equal sections, the probability of landing on blue first and then green is P(blue) × P(green) = (1/4) × (1/4) = 1/16.

Front

What is the probability of picking a blue marble, replacing it, and then picking a red marble?

Back

If there are 3 blue marbles and 4 red marbles, the probability is P(blue) × P(red) = (3/7) × (4/7) = 12/49.

Front

What is the probability of picking a green marble first and a red marble second without replacement?

Back

If there are 7 green marbles and 3 red marbles in a total of 20 marbles, the probability is P(green first) × P(red second) = (7/20) × (3/19) = 21/380.