Introductory Statistics

Lesson 3.2 B

Objectives:

SSBAT use the multiplication rule to find the probability of 2 events occurring in sequence.

SSBAT use the multiplication rule to find conditional probabilities.

Review.

Independent Events The probability of the 1st event does NOT affect the probability of the 2nd event.

Dependent Events The 1st event affects the probability of the 2nd event.

Multiplication Rule

Used to find the probability of 2 events, A and B, occurring in sequence

There are 2 cases:- A and B are Independent Events- A and B are Dependent Events

Multiplication Rule and Independent Events

If A and B are Independent events then

P(A and B) = P(A) ∙ P(B)

Examples: A and B are Independent Events

1. A coin is tossed and a die is rolled. Find the probability of getting a head and then rolling a 6.

P(H and 6) = P(H) ∙ P(6)

P(H and 6) = ∙

P(H and 6) = or 0.083

2. The following marbles are in a bag. 5 Red, 8 Yellow, 10 Blue, 13 Green

A person will roll a die and choose one marble out of the bag. Find the Probability of rolling an even

number and choosing a Red or Blue Marble.

P(Even and R or B) = P(Even) ∙ P(Red or Blue)

P(Even and R or B) = ∙

P(Even and R or B) =

P(Even and R or B) = 0.208

3. Three dice are tossed. Find the probability of getting a four on each die.

P(4, 4, 4) = P(4) · P(4) · P(4)

P(4, 4, 4) = · ·

P(4, 4, 4) =

P(4, 4, 4) = 0.005

4. The probability that a particular knee surgery is successful is 0.85. Find the probability that 2 knee surgeries are successful.

P(success and success) = P(S) · P(S)

P(S and S) = (0.85)(0.85)

P(S and S) = 0.7225

5. The probability that a particular knee surgery is successful is 0.85. Find the probability that both surgeries are not successful.

Probability of Not Successful is 1 – 0.85 = 0.15

P(Not and Not) = P(Not) · P(Not)

P(Not and Not) = (0.15)(0.15)

P(Not and Not) = 0.0225

6. The probability that a particular knee surgery is successful is 0.85. Find the probability that the first one is successful and the second one is not successful.

P(Success and Not) = P(Success) · P(Not)

P(Success and Not) = (0.85)(0.15)

P(Success and Not) = 0.1275

Multiplication Rule and Dependent events

If A and B are Dependent events then

P(A and B) = P(A) ∙ P(B|A)

Examples: A and B are Dependent Events

1. Two cards are selected from a deck of cards. The first card is not replaced. Find the probability of selecting a king and then selecting a queen.

P(K and then Q) = P(K) ∙ P(then Q)

P(K and then Q) = ∙

P(K and then Q) =

P(K and then Q) ≈ 0.006

2. Two cards are selected from a deck of cards. The first card is not replaced. Find the probability they are both hearts.

P(H and then H) = P(H) ∙ P(then H)

P(H and then H) = ∙

P(H and then H) =

P(H and then H) ≈ 0.059

Complete Worksheet 3.2 B