A bag has eight balls labeled A, B, C, D, E, F, G, and H. 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 A to D. If there is more than one element in the set, separate them with commas. Samplespace: Event of choosing a letter from A to D:

Respuesta :

We will have the following:

All the outcomes for the event of choosing a letter from A to D are:

[tex]\frac{4}{8}=0.5[/tex]

So half the times a ball is picked there should be one from letter A to D.

***Explanation***

We have the following set:

[tex]\mleft\lbrace A,B,C,D,E,F,G,H\mright\rbrace[/tex]

So, the set has a magnitude of 8 [Since it has 8 components].

When we pick any given value from the set we will have that we will have to pick 1 value from the total set, that is:

[tex]\frac{1}{8}[/tex]

But, when we are asked of the event of taking specific values from to D we are asked to pick 4 specific values:

[tex]\mleft\lbrace A,B,C,D\mright\rbrace[/tex]

That set has a magnitude of 4. So, in order to determine the event of picking a value from the second set on the first set, we will have:

[tex]p=\frac{4}{8}\Rightarrow p=\frac{1}{2}\Rightarrow p=0.5[/tex]

This event is represented by "p" the probability of that happening. So, the probability of the event happening [Selecting one of the balls of the specific set] is 1/2; in other words, each time you pick there is a 50% chance you will get one of the values of the smaller set.