50. Probability of Disjoint and Overlapping Events

Front

What is the Addition Rule in probability?

Back

The Addition Rule states that for any two events A and B, the probability of either A or B occurring is given by: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Front

What is the probability of drawing a red or blue marble from a bag containing 3 red and 4 blue marbles out of 12?

Back

The probability is P(red or blue) = (3/12) + (4/12) = 7/12.

Front

What are overlapping events in probability?

Back

Overlapping events are two events that have some outcomes in common.

Front

What is the formula for the probability of disjoint (mutually exclusive) events?

Back

For disjoint events A and B, the probability is given by: P(A or B) = P(A) + P(B).

Front

Define disjoint (mutually exclusive) events.

Back

Disjoint (mutually exclusive) events are events that cannot occur at the same time.

Front

How do you calculate the probability of either event A or event B when they are overlapping?

Back

Use the formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Front

What is the probability of drawing a number less than five or a shaded number if the options are 4/8 + 4/8 - 2/8?

Back

The probability is calculated as P(shaded number or number less than five) = 4/8 + 4/8 - 2/8.

Front

What is the probability of independent events?

Back

For independent events A and B, the probability of both A and B occurring is given by: P(A ∩ B) = P(A) * P(B).

Front

What is the difference between independent and dependent events?

Back

Independent events do not affect each other's outcomes, while dependent events do.

Front

What is the probability of drawing a red marble from a bag of 12 marbles containing 3 red marbles?

Back

The probability is P(red) = 3/12 = 1/4.