3
lesson pretestMultiple Choice

Pretest

Question 3 • Mathematics II

Which events are independent? Choose three correct answers.

Answer
A
Roll a number cube, and then roll the same number cube again.
B
Take a marble out of a bag, and then take a second marble out of the bag.
C
Remove a card from a deck, and then remove a second card.
D
Flip a coin, and then flip the coin a second time.
E
Draw a card from a deck, replace it, and then draw a second card.

Explanation

Two events are independent when the first event does not change the probability of the second. Each coin flip in A and each number-cube roll in B is a new random trial, so the first result does not affect the next. In D, replacing the card restores the deck before the second draw, so its probabilities stay the same. In C and E, the first item is not replaced, which changes what remains and affects the second draw.

AI-written and checked against the verified answer.

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