Addition & Multiplication Rule

Front

What is the Addition Rule in probability?

Back

The Addition Rule states that the probability of the occurrence of at least one of two events is equal to the sum of their individual probabilities minus the probability of their intersection: P(A or B) = P(A) + P(B) - P(A and B).

Front

What is the Multiplication Rule in probability?

Back

The Multiplication Rule states that the probability of the occurrence of two independent events is the product of their individual probabilities: P(A and B) = P(A) * P(B).

Front

Define independent events in probability.

Back

Independent events are two 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

Define dependent events in probability.

Back

Dependent events are two events where the occurrence of one event affects the occurrence of the other. For example, drawing two marbles from a bag without replacement.

Front

What is the formula to calculate the probability of 'A or B'?

Back

P(A or B) = P(A) + P(B) - P(A and B).

Front

What is the formula to calculate the probability of 'A and B' for independent events?

Back

P(A and B) = P(A) * P(B).

Front

If a bag contains 5 red marbles and 3 blue marbles, what is the probability of drawing a red marble?

Back

P(Red) = Number of Red Marbles / Total Marbles = 5 / (5 + 3) = 5/8.

Front

What is the probability of drawing a blue marble after drawing a red marble without replacement?

Back

If a red marble is drawn first, the probability of drawing a blue marble next is P(Blue) = Number of Blue Marbles / Remaining Marbles = 3 / (5 + 3 - 1) = 3/7.

Front

How do you find the probability of selecting a student who takes either French or Algebra?

Back

Use the Addition Rule: P(French or Algebra) = P(French) + P(Algebra) - P(French and Algebra).

Front

What is the probability of drawing a red marble, then a blue marble, then a green marble with replacement?

Back

P(Red, Blue, Green) = P(Red) * P(Blue) * P(Green) = (5/12) * (4/12) * (3/12) = 60/1728 = 5/144.