7.06 The General Multiplication Rule Standard P1 Apply probability concepts to calculate the probability of events.

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7.06 The General Multiplication Rule Standard P1 Apply probability concepts to calculate the probability of events

The General Multiplication Rule For A and B independent, we had: P(A and B) = P(A) × P(B) Rearranging the conditional probability equation, we get the General Multiplication Rule: P(A and B) = P(A) × P(B | A) Equivalently, P(A and B) = P(B) × P(A | B)

The General Multiplication Rule Mr. C needs two students to help him with a science demonstration for his class of 18 girls and 12 boys. He randomly chooses one student who comes to the front of the room. He then chooses a second student from those still seated. What is the probability that both students chosen are girls? P(Girl 1 and Girl 2) = P(Girl 1) . P(Girl 2|Girl 1)

Defective Computers Example In a shipment of 20 computers, 4 are defective. Three computers are randomly selected and tested. What is the probability that all three are defective if the first and second ones are not replaced after being tested? P(defective, defective, defective)

Defective Computers continued In the same shipment of 20 computers, 4 are defective. Three computers are randomly selected and tested. What is the probability that the first defective one is the third one? P(good, good, defective)

Defective Computers continued In the same shipment of 20 computers, 4 are defective. Three computers are randomly selected and tested. What is the probability that at least one of the computers is defective? P(at least one defective) = 1 – P(none defective) = 1 – P(good, good, good)

Probability Ya gotta think! and practice. Try the problems