Please explain how you got your answers! (: Solve the problem by using the counting principle.

ADrapery is sold in 4 different fabrics. Each fabric comes in 13 different patterns. Each pattern is offered in 9 different colors. How many fabric-pattern-color combinations are there?

BA shelf hold 3 novels, 2 biographies, and 1 history book. Two students in turn choose a book at random. What is the probability that the student choose the following?

both novels

A1/4
B1/2
C1/5
D1/3

A shelf hold 3 novels, 2 biographies, and 1 history book. Two students in turn choose a book at random. What is the probability that the student choose the following?

both biographies

A1/15
B1/20
C1/5
D1/3

A shelf hold 3 novels, 2 biographies, and 1 history book. Two students in turn choose a book at random. What is the probability that the student choose the following?

a history, then a novel

A1/2
B1/5
C1/10
D1/15

Question

18-05-2016
Mathematics

Answered

Please explain how you got your answers! (: Solve the problem by using the counting principle.

ADrapery is sold in 4 different fabrics. Each fabric comes in 13 different patterns. Each pattern is offered in 9 different colors. How many fabric-pattern-color combinations are there?

BA shelf hold 3 novels, 2 biographies, and 1 history book. Two students in turn choose a book at random. What is the probability that the student choose the following?

both novels

A1/4
B1/2
C1/5
D1/3

A shelf hold 3 novels, 2 biographies, and 1 history book. Two students in turn choose a book at random. What is the probability that the student choose the following?

both biographies

A1/15
B1/20
C1/5
D1/3

A shelf hold 3 novels, 2 biographies, and 1 history book. Two students in turn choose a book at random. What is the probability that the student choose the following?

a history, then a novel

A1/2
B1/5
C1/10
D1/15

Verified Answer :

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nobillionaireNobley nobillionaireNobley · Answer 1 · 2016-05-26T23:58:42-04:00

AThe number of fabric-pattern-color combinations is 4 13 9 = 468

B. P(1st choice) = no of novels / total books = 3/6 = 1/2
    P(2nd choice) = no of remaining novels/ total remaining books = 2/5
    P(both novels) = 1/2 2/5 = 1/5 (without replacement assumed)

C. P(1st choice) = no of biographies / total books = 2/6 = 1/3
    P(2nd choice) = no of remaining biographies/ total remaining books = 1/5
    P(both biographies) = 1/3 1/5 = 1/15 (without replacement assumed)

D. P(1st choice) = no of history books / total books = 1/6
    P(2nd choice) = no of novels/ total remaining books = 3/5
    P(a history, then a novel) = 1/6 * 3/5 = 1/10 (without replacement assumed)