subject: Mulitplication Probability [print this page] Probability is the likelihood of the occurrence of an event. An event is a one or more possible outcomes of a certain experiment. 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. An event consisting of more than one simple event is called compound event.
In probability, the range is defined as in between the values. However, in this article we will discuss about some useful and more interesting probability problems with easy steps. Before starting with probability, we need to know what is probability? Probability is nothing but an event occurs when you are doing some test. It is a study of probable outcomes or chances of an incident happening.
Multiplication rule for two events:
If A and B are two events then; P(A and B) = P(A) P(B)
Multiplication rule for three events:
If A, B, and B are three events then; P(A and B and C) = P(A) P(B) P(C)
Multiplication Probability - Example Problems
Example 1: A bag contains 15 dames and 15 quarters. If two coins are drawn at one by one with replacement, what is the probability of getting dame and quarter?
Solution:
Lest S be the sample space, n(S) = 15 + 15 = 30
A be the event of drawing dame, n(A) = 15
B be the event of drawing quarter, n(B) = 15
P(A) = (n(A))/(n(S)) = 15/30 = 1/2
P(B) = (n(B))/(n(S)) = 15/30 = 1/2
P(A and B) = P(A) P(B) = 1/2 1/2 = 1/4
P(dame and quarter) = 1/4
Example 2: A bag has 10 hundred dollar bills, 10 fifty dollar bills and 10 twenty dollar bills. If three bills are drawn at one by one without replacement, what is the probability of getting twenty, fifty and hundred dollar bills?
Solution:
Lest S be the sample space, n(S) = 10 + 10 + 10 = 30
A be the event of drawing twenty dollar bills, n(A) = 10
B be the event of drawing fifty dollar bills, n(B) = 10
C be the event of drawing hundred dollar bills, n(C) = 10
P(A) = (n(A))/(n(S)) = 10/301/3
Now there are 29 bills remaining in the bag.
P(B) = (n(B))/(n(S)) = 10/29
Now there are 28 bills remaining in the bag.
P(C) = (n(C))/(n(S)) = 10/28 = 5/14
P(A and B and C) = P(A) P(B) P(C) = 1/3 10/29 5/14 = 50/1218
P(twenty and fifty and hundred) = 25/609
Multiplication Probability - Practice Problems
Problem 1: A bag has 10 dames and 12 quarters. If two coins are drawn at one by one without replacement, what is the probability of getting dame and quarter?
Problem 2: A bag has 9 hundred dollar bills, 7 fifty dollar bills and 5 twenty dollar bills. If three bills are drawn at one by one with replacement, what is the probability of getting twenty, fifty and hundred dollar bills?
