Question

which is a pair of independent events?
○ choosing one calendar date for sports practice and then choosing a back - up date
○ choosing one card from a deck and then choosing one card from another deck
○ choosing a pen to write with in class and then choosing another to let a friend use
○ choosing a first place and then a second place work of art

Explanation:

To determine independent events, we check if the outcome of one event affects the other.

• For "choosing one calendar date for sports practice and then choosing a back - up date", the first date choice affects the second (since we can't repeat the same date), so dependent.
• For "choosing one card from a deck and then choosing one card from another deck", the two decks are separate. The outcome of drawing a card from the first deck has no impact on drawing a card from the second deck.
• For "choosing a pen to write with in class and then choosing another to let a friend use", the first pen choice reduces the number of pens available for the second choice, so dependent.
• For "choosing a first place and then a second place work of art", the first choice affects the second (since the first - place work can't be second - place), so dependent.

Answer:

choosing one card from a deck and then choosing one card from another deck