Question

a bag has six balls labeled a, b, c, d, e, and f. one ball will be randomly picked, and its letter will be recorded as the outcome. give the sample space describing all possible outcomes. then give all of the outcomes for the event of choosing a letter from d to f. if there is more than one element in the set, separate them with commas. sample space: {} event of choosing a letter from d to f : {}

Explanation:

Step1: Define sample space

The sample space is the set of all possible outcomes. Here, the balls are labeled \(A\), \(B\), \(C\), \(D\), \(E\), \(F\). So, the sample space \(S=\{A,B,C,D,E,F\}\).

Step2: Identify event outcomes

The event is choosing a letter from \(D\) to \(F\). The letters in this range are \(D\), \(E\), \(F\). So the event set \(E = \{D,E,F\}\).

Answer:

Sample space: \(\{A,B,C,D,E,F\}\)
Event of choosing a letter from \(D\) to \(F\): \(\{D,E,F\}\)