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

Back

To find the total number of outcomes, multiply the number of outcomes for each event. A coin has 2 outcomes (heads or tails) and a die has 6 outcomes. Therefore, total outcomes = 2 * 6 = 12.

Front

What is the probability of drawing a second purple marble after drawing a blue marble from a bag containing 3 purple, 1 blue, and 1 yellow marble?

Back

After drawing the blue marble, there are 5 marbles left (3 purple, 1 yellow). The probability of drawing a purple marble next is 3/5.

Front

What is the probability of rolling an even number on a six-sided die three times in a row?

Back

The probability of rolling an even number (2, 4, or 6) is 3/6 or 1/2. Therefore, the probability of rolling an even number three times in a row is (1/2) * (1/2) * (1/2) = 1/8.

Front

If I flip a coin 10 times, how many times should I expect to get heads?

Back

On average, you should expect to get heads 5 times when flipping a coin 10 times, since the probability of heads is 1/2.

Front

What is the probability of drawing a violet ball first and a pink ball next from a bag containing 2 violet and 4 pink balls, if the first ball is replaced?

Back

The probability of drawing a violet ball first is 2/6. After replacing it, the probability of drawing a pink ball next is 4/6. Therefore, the combined probability is (2/6) * (4/6) = 8/36 = 2/9.

Front

What is an independent event in probability?

Back

An independent event is an event whose outcome does not affect the outcome of another event. For example, tossing a coin and rolling a die are independent events.

Front

What is a dependent event in probability?

Back

A dependent event is an event whose outcome is affected by the outcome of another event. For example, drawing cards from a deck without replacement.

Front

What is the multiplication rule in probability?

Back

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

Front

What is the addition rule in probability?

Back

The addition rule states that the probability of either of two mutually exclusive events occurring is the sum of their individual probabilities.