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The probability of picking a 4 first is 1/5 since there is one 4 in a total of five cards.
After picking the first card (4), there are now four cards remaining including a 7, so the probability of picking a 7 second is 1/4.
The total probability of picking a 4 and then a 7 is (1/5) * (1/4) = 1/20 = 5%.
So, the probability of picking a 4 and then picking a 7 is 5%.