Fred and Ed each have a bag of candy that contains a lemon drop (L), a cherry drop (C), and an orange drop (O). Each takes out one piece from their bag and eats it. What is the sample space of the possible pairs of candies eaten?

The sample space of the possible pairs of candies eaten is LL CL OO LC CC LO OC CO OL. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

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johanrusli johanrusli · Answer 2 · 2019-09-09T04:14:00+02:00

The sample space of the possible pairs of candies eaten is

{ ( L , L ) , ( L , C ) , ( L , O ) , ( C , L ) , ( C , C ) , ( C , O ) , ( O , L ) , ( O , C ) , ( O , O ) }

Further explanation

The probability of an event is defined as the possibility of an event occurring against sample space.

[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]

Permutation ( Arrangement )

Permutation is the number of ways to arrange objects.

[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]

Combination ( Selection )

Combination is the number of ways to select objects.

[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]

Let us tackle the problem.

Fred has a lemon drop (L), a cherry drop (C), and an orange drop (O).

Ed has a lemon drop (L), a cherry drop (C), and an orange drop (O).

Each takes out one piece from their bag and eats it.

The sample space of possible pairs of candies eaten is as follows:

Fred eats a lemon drop (L) , Ed eats a lemon drop ( L ) → ( L , L )

Fred eats a lemon drop (L) , Ed eats a cheery drop ( C ) → ( L , C )

Fred eats a lemon drop (L) , Ed eats a orange drop ( C ) → ( L , O )

Fred eats a cherry drop (L) , Ed eats a lemon drop ( L ) → ( C , L )

Fred eats a cherry drop (L) , Ed eats a cheery drop ( C ) → ( C , C )

Fred eats a cherry drop (L) , Ed eats a orange drop ( C ) → ( C , O )

Fred eats a orange drop (L) , Ed eats a lemon drop ( L ) → ( O , L )

Fred eats a orange drop (L) , Ed eats a cheery drop ( C ) → ( O , C )

Fred eats a orange drop (L) , Ed eats a orange drop ( C ) → ( O , O )

From the results above, we can conclude that the sample space is:

{ ( L , L ) , ( L , C ) , ( L , O ) , ( C , L ) , ( C , C ) , ( C , O ) , ( O , L ) , ( O , C ) , ( O , O ) }

Learn more

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation