Probability and Independence in Events

Front

What is the definition of probability?

Back

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1.

Front

What does it mean for two events to be independent?

Back

Two events are independent if the occurrence of one event does not affect the probability of the other event occurring.

Front

How do you calculate the probability of an event?

Back

The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Front

What is conditional probability?

Back

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

Front

If P(A) = 0.3 and P(B) = 0.5, what is P(A and B) if A and B are independent?

Back

P(A and B) = P(A) * P(B) = 0.3 * 0.5 = 0.15.

Front

What is the probability of drawing a red marble from a bag containing 6 red, 5 green, and 4 yellow marbles?

Back

The probability of drawing a red marble is P(Red) = 6 / (6 + 5 + 4) = 6 / 15 = 2 / 5.

Front

What is the probability of not selecting a club member if there are 138 students and 63 are in clubs?

Back

The probability of not selecting a club member is P(Not in club) = 63 / 138.

Front

How do you find the probability of multiple independent events occurring?

Back

To find the probability of multiple independent events occurring, multiply the probabilities of each individual event.

Front

What is the probability of selecting a specific number from a set of 10 numbers without replacement?

Back

The probability of selecting a specific number is 1 / 10 for the first selection, and if not replaced, it becomes 1 / 9 for the second selection.