Question

A deck of cards contains RED cards numbered 1, 2, 3, and BLUE cards numbered 1, 2, 3, 4, 5, 6. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even-numbered card, and O the event of drawing an odd card.

Drawing the Blue 4 is an example of which of the following events? Select all correct answers.

Select all that apply:

A. R OR O

B. B AND O

C. R OR E

D. R AND O

E. R′

F. E′

Please let me know if you'd like any changes or additions to this question.

Answer 1

The event of drawing the Blue 4 corresponds to drawing a blue card and an even-numbered card
`(\(B \cap E\))`. Among the given options, only the complement of drawing an even-numbered card (E') includes this event. Therefore, the correct answer is E'.

F. E′

Step-by-step explanation:

The event "Drawing the Blue 4" involves two conditions: drawing a blue card and drawing an even-numbered card, denoted as
`\(B \cap E\)`. Each option represents a combination of events involving red cards (R) and blue cards (B) as well as even (E) and odd (O) numbered cards.

Option A:
`(\(R \cup O\))` signifies drawing either a red card or an odd card. This does not encompass the event "Drawing the Blue 4" since it lacks the requirement of drawing a blue card.

Option B:
`(\(B \cap O\))` represents drawing a blue card and an odd card. However, it does not account for the even-numbered aspect of the event "Drawing the Blue 4."

Option C:
`(\(R \cup E\))` denotes drawing either a red card or an even-numbered card. This fails to include the condition of drawing a blue card.

Option D:
`(\(R \cap O\))` implies drawing both a red card and an odd card, excluding the possibility of drawing a blue card or an even-numbered card.

Option E: (R') represents the complement of drawing a red card, which is irrelevant to the event "Drawing the Blue 4."

Option F: (E') signifies the complement of drawing an even-numbered card, which precisely captures the event "Drawing the Blue 4" by including both the blue card and even-numbered card conditions. Therefore, the correct answer is E'.