Multiplication Rule for Probability

Front

What is the Multiplication Rule for Probability?

Back

The Multiplication Rule states that the probability of two independent events occurring together is the product of their individual probabilities. If A and B are independent events, then P(A and B) = P(A) * P(B).

Front

Define independent events in probability.

Back

Independent events are two or more events where the occurrence of one event does not affect the occurrence of the other. For example, flipping a coin and rolling a die are independent events.

Front

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

Back

For two independent events A and B, the probability is calculated as P(A and B) = P(A) * P(B).

Front

Calculate the probability of rolling a 3 on a die and flipping heads on a coin.

Back

P(rolling a 3) = \frac{1}{6}, P(flipping heads) = \frac{1}{2}. Therefore, P(rolling a 3 and flipping heads) = \frac{1}{6} * \frac{1}{2} = \frac{1}{12}.

Front

What is the probability of drawing a red card from a standard deck of cards?

Back

There are 52 cards in total, with 26 red cards. Therefore, P(drawing a red card) = \frac{26}{52} = \frac{1}{2}.

Front

If the probability of event A is \frac{1}{4} and event B is \frac{1}{3}, what is the probability of both events occurring?

Back

Using the Multiplication Rule: P(A and B) = P(A) * P(B) = \frac{1}{4} * \frac{1}{3} = \frac{1}{12}.

Front

What is the difference between dependent and independent events?

Back

Dependent events are events where the outcome of one event affects the outcome of another. Independent events do not influence each other.

Front

Calculate the probability of drawing a heart and then drawing a spade from a deck of cards without replacement.

Back

P(drawing a heart) = \frac{13}{52}, P(drawing a spade after a heart) = \frac{13}{51}. Therefore, P(heart and spade) = \frac{13}{52} * \frac{13}{51} = \frac{169}{2652}.

Front

What is the probability of flipping two coins and getting two heads?

Back

P(heads on first coin) = \frac{1}{2}, P(heads on second coin) = \frac{1}{2}. Therefore, P(two heads) = \frac{1}{2} * \frac{1}{2} = \frac{1}{4}.

Front

Explain the concept of conditional probability.

Back

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