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In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won? What is the probability that one will have at least three draws before one picks a heart?
- a)1/2
- b)9/16
- c)11/16
- d)13/16
- e)15/16
Correct answer is option 'B'. Can you explain this answer?
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In a certain game, you pick a card from a standard deck of 52 cards. I...
A full deck of 52 cards contains 13 cards from each of the four suits. The probability of drawing a heart from a full deck is 1/4. Therefore, the probability of “not heart” is 3/4.
P(at least three draws to win) = 1 – P(win in two or fewer draws)
Furthermore,
P(win in two or fewer draws) = P(win in one draw OR win in two draws)
= P(win in one draw) + P(win in two draws)
Winning in one draw means: I select one card from a full deck, and it turns out to be a heart. Above, we already said: the probability of this is 1/4.
P(win in one draw) = 1/4
Winning in two draws means: my first draw is “not heart”, P = 3/4, AND the second draw is a heart, P = 1/4. Because we replace and re-shuffle, the draws are independent, so the AND means multiply.
P(win in two draws) = (3/4) * (1/4) = 3/16
P(win in two or fewer draws) = P(win in one draw) + P(win in two draws)
= 1/4 + 3/16 = 7/16
P(at least three draws to win) = 1 – P(win in two or fewer draws)
= 1 – 7/16 = 9/16
Answer = B
Most Upvoted Answer
In a certain game, you pick a card from a standard deck of 52 cards. I...
Calculating the Probability of Having At Least Three Draws Before Picking a Heart:
- The probability of not drawing a heart on the first draw is 39/52 (since there are 39 non-heart cards out of 52 total cards).
- The probability of not drawing a heart on the second draw is also 39/52.
- Therefore, the probability of not drawing a heart on the first two draws is (39/52) * (39/52).
- The probability of drawing a heart on the third draw is 13/52 (since there are 13 hearts in a deck of 52 cards).
- The probability of having at least three draws before picking a heart is equal to 1 minus the probability of picking a heart on the first or second draw, which is 1 - [(13/52) + (39/52)*(39/52)].
- Simplifying the equation, we get 1 - [13/52 + 1521/2704] = 1 - (676/2704) = 2028/2704 = 9/16.
Therefore, the probability that one will have at least three draws before picking a heart is 9/16, which corresponds to option 'b'.
- The probability of not drawing a heart on the first draw is 39/52 (since there are 39 non-heart cards out of 52 total cards).
- The probability of not drawing a heart on the second draw is also 39/52.
- Therefore, the probability of not drawing a heart on the first two draws is (39/52) * (39/52).
- The probability of drawing a heart on the third draw is 13/52 (since there are 13 hearts in a deck of 52 cards).
- The probability of having at least three draws before picking a heart is equal to 1 minus the probability of picking a heart on the first or second draw, which is 1 - [(13/52) + (39/52)*(39/52)].
- Simplifying the equation, we get 1 - [13/52 + 1521/2704] = 1 - (676/2704) = 2028/2704 = 9/16.
Therefore, the probability that one will have at least three draws before picking a heart is 9/16, which corresponds to option 'b'.
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In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won? What is the probability that one will have at least three draws before one picks a heart?a)1/2b)9/16c)11/16d)13/16e)15/16Correct answer is option 'B'. Can you explain this answer?
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In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won? What is the probability that one will have at least three draws before one picks a heart?a)1/2b)9/16c)11/16d)13/16e)15/16Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won? What is the probability that one will have at least three draws before one picks a heart?a)1/2b)9/16c)11/16d)13/16e)15/16Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won? What is the probability that one will have at least three draws before one picks a heart?a)1/2b)9/16c)11/16d)13/16e)15/16Correct answer is option 'B'. Can you explain this answer?.
In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won? What is the probability that one will have at least three draws before one picks a heart?a)1/2b)9/16c)11/16d)13/16e)15/16Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won? What is the probability that one will have at least three draws before one picks a heart?a)1/2b)9/16c)11/16d)13/16e)15/16Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won? What is the probability that one will have at least three draws before one picks a heart?a)1/2b)9/16c)11/16d)13/16e)15/16Correct answer is option 'B'. Can you explain this answer?.
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