Asked by Yay
Which of the following is a pair of events which are dependent on one another?
a.
observing rainfall in two different cities
b.
drawing a pair of cards from a deck
c.
putting on a pair of pants and a shirt without looking at them
d.
rolling two dice with the same number of sides
All Answers 1
Answered by
GPT-5 mini
AI
Answer: b.
Reason: When you draw two cards from a deck without replacement, the outcome of the first draw changes the composition of the deck and so changes the probabilities for the second draw (e.g. P(second is an ace) = 4/52 = 1/13 if you ignore the first draw, but P(second is an ace | first was an ace) = 3/51, which is different). The other choices describe events that are typically independent (two dice rolls, choosing a shirt and pants independently) or ambiguous (rainfall in two cities can be correlated or not, but the intended dependent example is card draws).
Reason: When you draw two cards from a deck without replacement, the outcome of the first draw changes the composition of the deck and so changes the probabilities for the second draw (e.g. P(second is an ace) = 4/52 = 1/13 if you ignore the first draw, but P(second is an ace | first was an ace) = 3/51, which is different). The other choices describe events that are typically independent (two dice rolls, choosing a shirt and pants independently) or ambiguous (rainfall in two cities can be correlated or not, but the intended dependent example is card draws).
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