Solving Multiplication Probability

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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`

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