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You pick a card at random. Without putting the first card back, you pick a second card at random. \newline456456\newlineWhat is the probability of picking a 66 and then picking a 55? \newlineWrite your answer as a fraction or whole number.\newline ___\_\_\_

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Probability of independent and dependent eventsright chevron icon

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Q. You pick a card at random. Without putting the first card back, you pick a second card at random. \newline456456\newlineWhat is the probability of picking a 66 and then picking a 55? \newlineWrite your answer as a fraction or whole number.\newline ___\_\_\_
  1. Calculate total cards: Step 11: Calculate the total number of cards in a standard deck.\newlineThere are 5252 cards in a deck.
  2. Determine 66 probability: Step 22: Determine the probability of picking a 66 first.\newlineThere are 44 sixes in a deck of 5252 cards.\newlineProbability of first card being a 6=4526 = \frac{4}{52}.
  3. Calculate 55 probability: Step 33: Calculate the probability of picking a 55 next, without replacing the first card.\newlineAfter picking a 66, there are 5151 cards left, including 44 fives.\newlineProbability of second card being a 5=4515 = \frac{4}{51}.
  4. Multiply probabilities: Step 44: Multiply the probabilities of the two independent events.\newlineProbability of picking a 66 and then a 55 = (4/52)×(4/51)(4/52) \times (4/51).
  5. Simplify expression: Step 55: Simplify the expression.\newline(452)×(451)=162652=4663(\frac{4}{52}) \times (\frac{4}{51}) = \frac{16}{2652} = \frac{4}{663}.

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