Dependent Events

Objective: Find the probability of dependent events.

Standard Addressed: 2.7.11: D Use theoretical probability distributions to make judgments about the

likelihood of various outcomes in uncertain situations.

KNOWING THE OUTCOME

OF ONE EVENT CAN

AFFECT THE PROBABILITY

OF ANOTHER EVENT

If one event does affect the occurrence of the other event, the events are dependent.

Probability of Dependent Events

Events A and B are dependent events if and only if P(A and B) = P (A) x P(B).

SOMETIMES THE PROBABILITY OF THE SECOND EVENTCHANGES DEPENDING ON THE OUTCOME OF THE FIRST EVENT.

AN ADDITION TO THE NOTEPACKET:

Ex. 2 A bag contains 12 blue disks and 5 green disks. For each case below, find the probability of selecting a green disk on the first draw and

a green disk on the second draw.

a. The first disk is replaced.

5/17 * 5/17 = 25/289 = 8.7%

b. The first disk is NOT replaced.

5/17 * 4/16 = 20/272 = 7.35%

Ex. 3 A bag contains 8 red disks, 9 yellow disks, and 5 blue disks. Two consecutive draws are made from the bag WITHOUT replacement of the

first draw. Find the probability of each event.

  a. red first, red second

8/22 * 7/21 = 56/462 = 12.12%

b. yellow first, blue second

9/22 * 5/21 = 45/462 = 9.7%

c. blue first, blue second

5/22 * 4/21 = 20/462 = 4.3%

d. red first, blue second

8/22 * 5/21 = 40/462 = 8.7%

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