To find the complement of not picking a 6 from a standard deck of 52 cards, we first need to determine the total number of favorable outcomes and then calculate the complement.
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Total number of cards in the deck: There are 52 cards in total.
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Number of favorable outcomes for not picking a 6: There are 4 sixes in the deck (one from each suit: hearts, spades, diamonds, clubs). So, the number of cards that are not a 6 is: \[ 52 - 4 = 48 \]
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Probability of not picking a 6: The probability of not picking a 6 is given by the number of non-6 cards divided by the total number of cards: \[ P(\text{not picking a 6}) = \frac{48}{52} \]
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Complement of not picking a 6 (which is picking a 6): The complement probability can be found by subtracting the probability of not picking a 6 from 1: \[ P(\text{picking a 6}) = 1 - P(\text{not picking a 6}) = 1 - \frac{48}{52} \] \[ = \frac{52}{52} - \frac{48}{52} = \frac{4}{52} \]
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Simplifying the fraction: The fraction \(\frac{4}{52}\) can be simplified by dividing both the numerator and the denominator by their GCD, which is 4: \[ \frac{4 \div 4}{52 \div 4} = \frac{1}{13} \]
Thus, the complement of not picking a 6 is \(\frac{1}{13}\).