select the correct answer. ross was playing with a deck of cards. he took out all the diamond suit cards…

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)

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)

Answer

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}