I am lost with these two problems...
Problem #1
Write a sample space for the given experiment
A box contains 3 blue cards numbered through 3, 4green cards numbered through 4. A blue card is picked , followed by a green card.
Problem #2
Write the indicated even in set notation
The event that Charlie is selected as a board member when three board memebers are selected at random from the following group: Allison, betty, dave and emily
[the possible outcomes can be represented as follows
ABC ABD ABE ACE ACE
ADE BCD BCE BDE CDE]
Problem #1:
To write the sample space for the given experiment, we need to list all the possible outcomes.
In this case, we are picking a blue card followed by a green card. We have 3 blue cards numbered through 3, and 4 green cards numbered through 4.
The sample space will consist of all possible pairs, where the first element is a blue card and the second element is a green card.
Sample space for the experiment:
{(1B, 1G), (1B, 2G), (1B, 3G), (2B, 1G), (2B, 2G), (2B, 3G), (3B, 1G), (3B, 2G), (3B, 3G)}
To obtain this, you simply pair each blue card with each green card one by one.
Problem #2:
To write the indicated event, which is the event that Charlie is selected as a board member when three board members are selected at random from the group (Allison, Betty, Dave, and Emily), we need to identify all the outcomes where Charlie is selected.
Possible outcomes:
ABC, ABD, ABE, ACE, ACE, ADE, BCD, BCE, BDE, CDE
In set notation, we use curly brackets {} to denote a set. The event that Charlie is selected can be represented as:
{ABC, ABD, ABE, ACE, ACE, ADE}
Here, the set contains all possible combinations where Charlie (C) is selected.