Probability of Compound Events

Front

What is the definition of a compound event in probability?

Back

A compound event is an event that consists of two or more simple events. It can be formed by combining simple events using the operations of 'and' (intersection) or 'or' (union).

Front

How do you calculate the probability of two independent events occurring together?

Back

To calculate the probability of two independent events A and B occurring together, multiply their individual probabilities: P(A and B) = P(A) * P(B).

Front

What is the probability of rolling a die and getting an even number?

Back

The probability of rolling an even number (2, 4, or 6) on a standard die is 3/6 or 1/2.

Front

What is the formula for calculating the probability of the union of two events?

Back

The probability of the union of two events A and B is given by: P(A or B) = P(A) + P(B) - P(A and B).

Front

What is the probability of drawing a card from a standard deck and getting a heart?

Back

The probability of drawing a heart from a standard deck of 52 cards is 13/52 or 1/4.

Front

What does it mean for two events to be mutually exclusive?

Back

Two events are mutually exclusive if they cannot occur at the same time. For example, rolling a 3 and rolling a 4 on a single die roll are mutually exclusive events.

Front

How do you find the expected value in a probability scenario?

Back

The expected value is calculated by multiplying each possible outcome by its probability and summing all these products: E(X) = Σ [x * P(x)].

Front

What is the probability of spinning a spinner divided into 4 equal sections and landing on red?

Back

If the spinner is divided into 4 equal sections, the probability of landing on red is 1/4.

Front

What is the probability of drawing two marbles from a bag containing 3 red and 2 blue marbles without replacement?

Back

The probability of drawing a red marble first and then a blue marble is (3/5) * (2/4) = 3/10.

Front

What is the concept of conditional probability?

Back

Conditional probability is the probability of an event occurring given that another event has already occurred, denoted as P(A|B).