Multiplication Formula for Dependent Events
The multiplication formula for dependent events is a Grade 7 probability concept in Big Ideas Math Advanced 2, Chapter 15: Probability and Statistics. For dependent events A and B, P(A and B) equals P(A) times P(B after A), where P(B after A) is the conditional probability after A has occurred. For example, the probability of drawing a King then a Queen without replacement is 4/52 times 4/51.
Key Concepts
For dependent events A and B: $$P(A \text{ and } B) = P(A) \times P(B \text{ after } A)$$.
Where $P(B \text{ after } A)$ is the conditional probability of event B occurring given that event A has already occurred.
Common Questions
What is the formula for probability of dependent events?
For dependent events A and B, P(A and B) equals P(A) times P(B after A). The second probability uses the updated sample space after the first event has occurred.
How is the multiplication rule different for dependent versus independent events?
For independent events, P(A and B) equals P(A) times P(B). For dependent events, you must use the conditional probability P(B after A), which accounts for the changed conditions after A occurs.
How do you calculate probability when drawing cards without replacement?
For the first draw, use the original counts. For the second draw, reduce both the total cards and favorable cards by 1 if the first draw was favorable, then multiply the two probabilities.
What textbook covers the multiplication formula for dependent events in Grade 7?
Big Ideas Math Advanced 2, Chapter 15: Probability and Statistics covers the multiplication formula for both independent and dependent compound events.