Question

select the correct answer. ross was playing with a deck of cards. he took out all the diamond suit cards having a value greater than 2 and less than 10. he kept them upside down on a table and picked a card at random. let event a be picking up a card with an odd number as its value. let event b be picking up a card with a value that is a multiple of three. which of the following outcomes represents the complement of b? (3, 6, 9) (3, 5, 7, 9) (4, 6, 8) (4, 5, 7, 8)

Explanation:

Step1: Identify the sample - space of diamond cards with values 3 - 9

The diamond cards with values greater than 2 and less than 10 are 3, 4, 5, 6, 7, 8, 9. So the sample - space of diamond cards in this range has 7 elements.

Step2: Define event B

Event B is picking a card with a value that is a multiple of three. Among the values 3, 4, 5, 6, 7, 8, 9, the multiples of three are 3, 6, 9.

Step3: Find the complement of B

The complement of an event B, denoted as $\overline{B}$, contains all the elements in the sample - space that are not in B. The sample - space of diamond cards with values 3 - 9 is {3, 4, 5, 6, 7, 8, 9}, and B = {3, 6, 9}. So $\overline{B}=\{4,5,7,8\}$

Answer:

{4, 5, 7, 8}