5. given a standard deck of playing cards, which of the following events cannot happen together? selecting a…

5. given a standard deck of playing cards, which of the following events cannot happen together? selecting a heart. a selecting a 5. b selecting a red card. c selecting a queen. d

5. given a standard deck of playing cards, which of the following events cannot happen together? selecting a heart. a selecting a 5. b selecting a red card. c selecting a queen. d

Answer

Brief Explanations:

To determine which events are mutually exclusive, we analyze each pair:

  • A (heart) and C (red card): Hearts are red, so they can occur together.
  • A (heart) and B (5): There is a 5 of hearts, so they can occur together.
  • A (heart) and D (queen): There is a queen of hearts, so they can occur together.
  • B (5) and C (red card): There are red 5s (hearts and diamonds), so they can occur together.
  • B (5) and D (queen): A card can't be both a 5 and a queen (a 5 has rank 5, a queen has rank queen—no overlap in rank), so these events are mutually exclusive.
  • C (red card) and D (queen): There are red queens (hearts and diamonds), so they can occur together.

Answer:

B. Selecting a 5, D. Selecting a queen