An event is a one or more possible outcomes from an experiment. An event consisting of one or more simple events is called compound event. An event is called independent event if one event does not affect the other event. An event is called dependent event if one event does affect the other event. Two events cannot happen at the same time, they are called mutually exclusive events.
Probability Compound Events – Formulas
Probability of two independent events:
P(A and B) = P(A) · P(B)
Probability of two dependent events:
P(A and B) = P(A) · P(B following A)
Probability of two mutually exclusive events:
P(A or B) = P(A) + P(B)
Probability Compound Events - Examples
Example 1: Find the probability of rolling a dice and getting a 5 on each one.
Solution:
These events are independent.
P(5) · P(5) = (1/6) · (1/6) or (1/36)
Therefore, probability is 1/36.
Example 2: A box contains pen, pencil, and eraser. Find the probability of choosing first pen and then, without replacing the pen, choosing a pencil.
Solution:
These events are dependent.
The first probability is (1/3).
The probability of choosing a pencil is (1/2) since there are now only pen and eraser are left.
The probability of both is
(1/3) · (1/2) = (1/6)
Example 3: What is the probability of choosing a queen and seven with replacement?
Solution:
P(Queen) = 4/52
P(Seven) = 4/52
P(Queen and Seven) = P(Q) · P(S)
= 4/52 · 4/52
= 16/2704
=1/169
Example 4: A box contains 5 rose, 7 brown, 4 black and 8 white marbles. A marble is chosen at random from the box. After replacing it, a second marble is chosen. What is the probability of choosing a brown and a white marble?
Solution:
P(Brown) = 7/24
P(White) = 8/24 = 1/3
P(Brown and White) = P(Brown) · P(White)
= 7/24 · 1/3 = 7/72
Probability Compound Events - Practice problems
Problem 1: What is the probability of choosing a seven and king of diamond with replacement?
Answer: 1/676
Problem 2: A coin is tossed and a 6-sided die is rolled. Find the probability of tail and 5.
Answer: 1/12
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