Unit 6: Probability - Lesson 8

Unit 6: Probability

Lesson 8 - Dependent Events

Dependent Events

• If the outcomes of one event affects the outcome of another event, the events are called Dependent Events

• Ex: You have a bag, you pick one marble but do not replace it, and then pick another.

Dependent Events

If two events A and B are dependent, then the probability of both events occurring is the product of the P(A) and Probability of B after A occurs.

P(A and B) = P(A) x P(B following A)

OR

P(A and B) = P(A) x P(B|A)

Multiple Choice

What type of event is happening in the diagram?

• Independent Event, they are replacing the marble

• Dependent Event, they are not replacing the marble

• Independent Event, they are not replacing the marble

• Dependent Event, they are replacing the marble

Calculate Probability

• Determine P(A)

• Determine the probability of B happening if A has already happened.

• Ex: Drawing a Marble from a Bag [4 B, 1 R] No Replacement.

• P(A) = P(Blue) -> 4/5

• Marbles in the bag: 3 B, 1 R

• P(B) = P(Red) -> 1/4

• P(B,R) = 4/5 x 1/4 = 4/20 = 1/5

Think

• Ex: 5 marbles in a bag [2 blue 3 red] The probability of drawing a marble twice, without replacement.

• You can draw a red marble. Marbles in the bag=4 [2 R, 2 B]

• You can draw a blue marble. Marbles in the bag=4 [3 R, 1 B]

Multiple Choice

Determine the probability of drawing a red marble first, then drawing a green marble second without replacement.

• P(Red) = 3/12 = 1/4

  P(Green|Red) = 2/11

  P(R) + P(G | R) = 1/4 + 2/11 =

  19/44

• P(Red) = 3/12 = 1/4

  P(Green) = 2/12 = 1/6

  P(R and G) = 1/4 + 1/6 = 5/12

• P(Red) = 3/12 = 1/4

  P(Green|Red) = 2/11

  P(R) x P(G | R) = 1/4 x 2/11 =

  2/44 = 1/22

• P(Red) = 3/12 = 1/4

  P(Green) = 2/12 = 1/6

  P(R and G) = 1/4 x 1/6 = 1/24

Multiple Choice

A penny is tossed and a number cube is rolled. P(Tails and 3). Is it Independent or Dependent?

• Independent, one outcomes doesn't affect the other.

• Dependent, one outcomes does affect the other.

• Independent, one outcomes does affect the other.

• Dependent, one outcomes doesn't affect the other.

Multiple Choice

A penny is tossed and a number cube is rolled. P(Tails and 3). Which formula should we use?

• P(A & B) = P(A) x P(B|A)

• P(A & B) = P(A) x P(B)

• P(A & B) = P(A) + P(B)

Multiple Choice

A penny is tossed and a number cube is rolled. P(Tails and 3). Dependent?

• P(Tails) = 1/2

  P(3) = 1/6

  P(T & 3) = 1/2 + 1/6 = 8/12 = 3/4

• P(Tails) = 1/2

  P(3) = 1/3

  P(T & 3) = 1/2 x 1/3 = 1/6

• P(Tails) = 1/2

  P(3) = 1/6

  P(T and 3) = 1/6 x 1/2 = 1/12

Poll

How are you feeling?