Conditional Probability And Independence

Front

What is 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.

Front

What is the formula for conditional probability?

Back

The formula for conditional probability is P(A|B) = P(A and B) / P(B), where P(A and B) is the probability of both A and B occurring.

Front

What does it mean for two events to be independent?

Back

Two events A and B are independent if the occurrence of one does not affect the probability of the other. Mathematically, this is expressed as P(A and B) = P(A) * P(B).

Front

How can you determine if two events are independent using probabilities?

Back

To determine if two events A and B are independent, check if P(A and B) = P(A) * P(B). If this equality holds, the events are independent.

Front

What is the probability of event A if P(A) = 2/5 and P(B) = 1/5, and P(A and B) = 2/25?

Back

The events A and B are independent because P(A and B) = P(A) * P(B) = (2/5) * (1/5) = 2/25.

Front

What is the meaning of P(A and B)?

Back

P(A and B) represents the probability that both events A and B occur simultaneously.

Front

What is the significance of the shaded region in a Venn diagram representing events A and B?

Back

The shaded region in a Venn diagram typically represents the intersection of events A and B, which is denoted as A and B or P(A and B).

Front

How do you calculate the probability of a compound event?

Back

To calculate the probability of a compound event, you can use the addition rule for mutually exclusive events or the multiplication rule for independent events.

Front

What is the probability of flipping a heads on a coin and then landing on yellow on a spinner if the probability of heads is 1/2 and yellow is 1/6?

Back

The probability is calculated as P(Heads) * P(Yellow) = (1/2) * (1/6) = 1/12.

Front

What is the formula for the total probability of an event?

Back

The total probability of an event can be calculated using the law of total probability, which states that P(A) = P(A|B)P(B) + P(A|not B)P(not B).