Solving Multiplication Probability
Discrete probability:
Discrete probability:
A random variable which will take a certain set of possible individual values and it will take positive integers. Positive integers mean 1, 2, and 3 .likewise. In probability theory the distribution of probability is called discrete probability. Probability mass function is used to characterize the discrete probability. The random variable xs distribution is discrete the we can call it as discrete random variable.
'sum_(u)^oo' Pr(X =u) = 1
Where u is the possible values for x. if any variable is discrete at least it is having some values that mean this set can be assumed non-zero probability.
Difference between Discrete Probability and Continuous Probability:
Let us show the difference between the discrete probability and continuous probability variable using some example. It is better to understand the variables.
1. If we have to select the members in a office whom are in the age between 30 and 40. In this we can select any members whom are in the age of 30 and 40. Here we will get some finite variable so it would be a continuous variable. Since the workers age could take on any value between 30 and 40 years.
2. Consider flipping a coin and get the count for number of heads. We can get the possible values between 0 and plus infinity. Whatever the probability to getting heads it can be lies between 0 and plus infinity. It is an example for discrete probability.
Example for Discrete Probability:
If we flip two coins we are having the possibilities are HH, HT, TH, and TT. Totally we are having four possibilities. The random variable X represents the number of heads which is the result for our experiment. Here x is a random variable so it will take the possible values 0, 1, and 2.So it is a discrete random variable.
Solving Multiplication Probability
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.
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)
Solving Multiplication Probability - Solving Example Problems
See these example problems, it will help you to understand about multiplication rule of probability.
Example 1: A bag contains 8 nickels and 6 dames. If two coins are drawn at random, what is the probability of getting nickel and dame with replacement?
Solution:
Lest S be the sample space, n(S) = 8 + 6 = 14
A be the event of drawing nickel, n(A) = 8
B be the event of drawing dame, n(B) = 6
P(A) = '(n(A))/(n(S))' = '8/14' = '4/7'
P(B) = '(n(B))/(n(S))' = '6/14' = '3/7'
P(A and B) = P(A) P(B) = '4/7' '3/7' = '12/49'
P(A and B) = '12/49'
Example 2: A jar contains 4 dark, 6 milk, and 8 bitter chocolates. If 3 chocolates are drawn at random, what is the probability of getting dark, milk and bitter chocolate without replacement?
Solution:
Lest S be the sample space, n(S) = 4 + 6 + 8 = 18
A be the event of drawing dark chocolate, n(A) = 4
B be the event of drawing milk chocolate, n(B) = 6
C be the event of drawing bitter chocolate, n(C) = 8
P(A) = '(n(A))/(n(S))' = '4/18''2/9'
P(B) = '(n(B))/(n(S))' = '6/18' = '1/3'
P(C) = '(n(C))/(n(S))' = '8/18' = '4/9'
P(A and B and C) = P(A) P(B) P(C) = '2/9' '1/3' '4/9' = '8/243'
P(dark and milk and bitter) = '8/243'
Solving Multiplication Probability - Solving Practice Problems
Solve these problems, it will help you to get practice on how to use the multiplication rule of probability.
Problem 1: A bag contains 4 nickels and 6 dames. If two coins are drawn at random, what is the probability of getting nickel and dame with replacement?
Problem 2: A jar contains 4 dark, 3 milk, and 2 bitter chocolates. If 3 chocolates are drawn at random, what is the probability of getting dark, milk and bitter chocolate?
Answer: 1) '6/25' 2) '8/81'
by: Omkar Nayak
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