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What is the probability of drawing at least one red card when you draw a card from a standard deck 4 times?

1) 0.205
2) 0.455
3) 0.682
4) 0.819

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1 Answer

5 votes

Final answer:

The probability of drawing at least one red card from a standard deck in 4 tries without replacement is 0.819, making option 4 the correct answer.

Step-by-step explanation:

The question is asking to calculate the probability of drawing at least one red card from a standard deck of 52 cards when drawing a card 4 times without replacement.

To solve this, we look at the complementary probability, which is the probability of not drawing a red card in any of the 4 draws.

Since there are 26 red cards in a standard deck, there are also 26 black cards. The probability of drawing a black card in the first draw is 26/52 or 1/2. If the first card drawn is black, there will be 25 black cards and 51 cards total remaining for the second draw, so the probability of drawing a black card again is 25/51.

Continuing this process for four draws, we get a probability chain for drawing all black cards:

(26/52) × (25/51) × (24/50) × (23/49).

To find the probability of drawing at least one red card, we subtract this chain of probabilities from 1:

1 - [(26/52) × (25/51) × (24/50) × (23/49)].

Calculating this gives us 0.819, which makes option 4) 0.819 the correct choice.

User Luis Cardoza Bird
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