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 EVENT
CHANGES 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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