Q:

A marble is selected from a bag containing eight marbles numbered 1 to 8The number on the marble selected will be recorded as the outcome.Consider the following events.Event A: The marble selected has a number of less than 4Event B: The marble selected has an even number.Give the outcomes for each of the following events.If there is more than one element in the set, separate them with commas.

Accepted Solution

A:
Answer: 'A or B'   =   {1,2,3,4,6,8} 'A and  B'   =    {2} The complement of A  =  {4,5,6,7,8)Step-by-step explanation:Here, the sample space of possible outcomes = { 1,2,3,4,5,6,7,8}Event A: The marble selected has a number of less than 4 So, favorable outcomes here=  {1,2,3)Event B: The marble selected has an even number.So, favorable outcomes here=  {2,4,6,8)Total number of outcomes in Event 'A or B' =  A U B  =   {1,2,3,4,6,8} ⇒ 'A or B'   =   {1,2,3,4,6,8} Total number of outcomes in Event 'A and  B' =  A ∩ B  =   {2} ⇒ 'A and  B'   =    {2} Now, The complement of A  = Sample Space  - Element in A                                                  = {4,5,6,7,8}⇒The complement of A  =  {4,5,6,7,8)