123ArticleOnline Logo
Welcome to 123ArticleOnline.com!
ALL >> Education >> View Article

Solving Multiplication Probability

Profile Picture
By Author: Pierce Brosnan
Total Articles: 127
Comment this article
Facebook ShareTwitter ShareGoogle+ ShareTwitter Share

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`

Comprehend more on about Logarithm Formulas and its Circumstances. Between, if you have problem on these topics Formula to Calculate Compound Interest Please share your views here by commenting.

Total Views: 127Word Count: 446See All articles From Author

Add Comment

Education Articles

1. Tested Tutor Reading Comprehension In Wellington: Enhancing Literacy Skills For Lifelong Learning
Author: khizar haider

2. Studyauracle
Author: Studyauracle

3. 10 Digital Marketing Tools You Must Use In 2025
Author: neetu

4. School Tutor Website In Palm Beach
Author: khizar haider

5. Studying Mbbs Abroad Is A Way To Successful Mbbs Career
Author: Mbbs Blog

6. Join Microsoft Dynamics 365 Courses – Online Training
Author: Pravin

7. Gcp Cloud Data Engineer Training | India
Author: naveen

8. Generative Ai For Devops Training Classes | Visualpath
Author: Visualpath

9. Best Az-305 | Azure Solutions Architect Expert Training
Author: gollakalyan

10. Tomorrow Starts With A Healthy Today
Author: Akshaya Patra

11. Gen Ai Training In Hyderabad | Best Generative Ai Training
Author: Susheel

12. Top Sap Ariba Training Institutes | Sap Ariba Training In Bangalore
Author: krishna

13. Safety & Health At Work - Qqi Level 5 Qualification
Author: johnnytorrt

14. School Tutor Website In Boynton Beach
Author: khizar haider

15. How To Become A Special Needs Tutor In Jacksonville
Author: khizar haider

Login To Account
Login Email:
Password:
Forgot Password?
New User?
Sign Up Newsletter
Email Address: