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You grab a card at random. Without putting the first card back, you grab a second card at random. \newlineWhat is the probability of grabbing a Queen and then grabbing a King? \newlineWrite your answer as a fraction or whole number. \newline ______

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Q. You grab a card at random. Without putting the first card back, you grab a second card at random. \newlineWhat is the probability of grabbing a Queen and then grabbing a King? \newlineWrite your answer as a fraction or whole number. \newline ______
  1. Determine total number of cards: Determine the total number of cards in a standard deck and the number of Queens and Kings.\newlineA standard deck of cards has 5252 cards, with 44 Queens and 44 Kings.
  2. Calculate probability of grabbing a Queen first: Calculate the probability of grabbing a Queen first.\newlineThe probability of grabbing a Queen first is the number of Queens divided by the total number of cards.\newlineP(Grabbing a Queen)=Number of QueensTotal number of cards=452P(\text{Grabbing a Queen}) = \frac{\text{Number of Queens}}{\text{Total number of cards}} = \frac{4}{52}
  3. Calculate probability of grabbing a King second without replacement: Calculate the probability of grabbing a King second without replacement.\newlineAfter grabbing a Queen, there are 5151 cards left and still 44 Kings.\newlineP(Grabbing a King second)=Number of KingsRemaining number of cards=451P(\text{Grabbing a King second}) = \frac{\text{Number of Kings}}{\text{Remaining number of cards}} = \frac{4}{51}
  4. Calculate combined probability of both events happening in sequence: Calculate the combined probability of both events happening in sequence.\newlineThe combined probability is the product of the probabilities of each individual event.\newlineP(Grabbing a Queen and then a King)=P(Grabbing a Queen)×P(Grabbing a King second)=(452)×(451)P(\text{Grabbing a Queen and then a King}) = P(\text{Grabbing a Queen}) \times P(\text{Grabbing a King second}) = \left(\frac{4}{52}\right) \times \left(\frac{4}{51}\right)
  5. Simplify the fraction: Simplify the fraction.\newlineP(Grabbing a Queen and then a King)=452×451=113×451=413×51=4663P(\text{Grabbing a Queen and then a King}) = \frac{4}{52} \times \frac{4}{51} = \frac{1}{13} \times \frac{4}{51} = \frac{4}{13 \times 51} = \frac{4}{663}

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