Question

1. an urn contains 5 distinct balls, labeled from 1 to 5. the experiment consists of selecting 2 balls from the urn, without replacement (first ball taken will not be placed back to the urn), and recording the sequence of ball numbers. a) list the elements of the sample space, s.

Explanation:

Step1: Understand sample - space concept

The sample - space is the set of all possible outcomes. When selecting 2 balls without replacement from 5 distinct balls labeled 1 to 5, we need to find all ordered pairs.

Step2: Calculate number of outcomes

The number of ways to select 2 balls out of 5 without replacement (permutations) is given by \(P(5,2)=\frac{5!}{(5 - 2)!}=\frac{5!}{3!}=5\times4 = 20\).

Step3: List the elements

The sample - space \(S=\{(1,2),(1,3),(1,4),(1,5),(2,1),(2,3),(2,4),(2,5),(3,1),(3,2),(3,4),(3,5),(4,1),(4,2),(4,3),(4,5),(5,1),(5,2),(5,3),(5,4)\}\)

Answer:

\(S=\{(1,2),(1,3),(1,4),(1,5),(2,1),(2,3),(2,4),(2,5),(3,1),(3,2),(3,4),(3,5),(4,1),(4,2),(4,3),(4,5),(5,1),(5,2),(5,3),(5,4)\}\)