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 ) }
<h3>Further explanation</h3>
The probability of an event is defined as the possibility of an event occurring against sample space.
![\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }](https://tex.z-dn.net/?f=%5Clarge%20%7B%20%5Cboxed%20%7BP%28A%29%20%3D%20%5Cfrac%7B%5Ctext%7BNumber%20of%20Favorable%20Outcomes%20to%20A%7D%7D%7B%5Ctext%20%7BTotal%20Number%20of%20Outcomes%7D%7D%20%7D%20%7D)
<h2>Permutation ( Arrangement )</h2>
Permutation is the number of ways to arrange objects.
![\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }](https://tex.z-dn.net/?f=%5Clarge%20%7B%5Cboxed%20%7B%5EnP_r%20%3D%20%5Cfrac%7Bn%21%7D%7B%28n%20-%20r%29%21%7D%20%7D%20%7D)
<h2>Combination ( Selection )</h2>
Combination is the number of ways to select objects.
![\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }](https://tex.z-dn.net/?f=%5Clarge%20%7B%5Cboxed%20%7B%5EnC_r%20%3D%20%5Cfrac%7Bn%21%7D%7Br%21%20%28n%20-%20r%29%21%7D%20%7D%20%7D)
Let us tackle the problem.
<em>Fred has a lemon drop (L), a cherry drop (C), and an orange drop (O).</em>
<em>Ed has a lemon drop (L), a cherry drop (C), and an orange drop (O).</em>
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 ) }
<h3>Learn more</h3>
<h3>Answer details</h3>
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation