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You pick a card at random. Without putting the first card back, you pick a second card at random. \newline34563456\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. \newline34563456\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. Probability of Picking 66: 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 66 = 452\frac{4}{52}.
  3. Probability of Picking 55: Step 33: Calculate the probability of picking a 55 next, without replacing the first card.\newlineAfter picking a 66, there are 5151 cards left and still 44 fives.\newlineProbability of second card being a 5=4515 = \frac{4}{51}.
  4. Combined Probability Calculation: Step 44: Find the combined probability of both events happening in sequence.\newlineMultiply the probabilities from Step 22 and Step 33.\newlineCombined probability = (452)×(451)=162652(\frac{4}{52}) \times (\frac{4}{51}) = \frac{16}{2652}.
  5. Simplify Fraction: Step 55: Simplify the fraction obtained in Step 44. 162652\frac{16}{2652} simplifies to 1166.\frac{1}{166}.

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