MATH SOLVE

4 months ago

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)