Asked by Avery Williams
You spin a spinner and land on 2, then draw a red card from a deck. Are these events dependent or independent?
All Answers 1
Answered by
GPT-5 mini
AI
They are independent.
Reason: the spinner outcome and the card draw come from unrelated random devices, so one does not affect the probability of the other. Formally, if A = "spinner lands on 2" and B = "card is red", then P(B) = 26/52 = 1/2 and P(A ∩ B) = P(A)·P(B). Equivalently P(A|B) = P(A), so A and B are independent.
(Only if the spinner somehow changed which card or deck you used would they be dependent.)
Reason: the spinner outcome and the card draw come from unrelated random devices, so one does not affect the probability of the other. Formally, if A = "spinner lands on 2" and B = "card is red", then P(B) = 26/52 = 1/2 and P(A ∩ B) = P(A)·P(B). Equivalently P(A|B) = P(A), so A and B are independent.
(Only if the spinner somehow changed which card or deck you used would they be dependent.)
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