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Twenty cards are numbered 1-20. You draw a card. Without replacing it, you draw a second card. Find the probability that the first card will be an even number and the second card drawn will be an even number.

Twenty cards are numbered 1−20 1-20 . You draw a card. Without replacing it, you draw a second card. Find the probability that the first card will be an even number and the second card drawn will be an even number.

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Full solution

Q. Twenty cards are numbered 1−20 1-20 . You draw a card. Without replacing it, you draw a second card. Find the probability that the first card will be an even number and the second card drawn will be an even number.
  1. Determine total even cards: Determine the total number of even cards in the deck. There are 1010 even numbers between 11 and 2020 (22, 44, 66, 88, 1010, 1212, 1414, 1100, 1111, 2020).
  2. Calculate first draw probability: Calculate the probability of drawing an even card on the first draw. Since there are 2020 cards in total and 1010 are even, the probability is 1020\frac{10}{20} or 12\frac{1}{2}.
  3. Calculate second draw probability: Calculate the probability of drawing an even card on the second draw without replacement. After drawing one even card, there are now 99 even cards left and 1919 cards in total. The probability for the second draw is therefore 919\frac{9}{19}.
  4. Multiply probabilities: Multiply the probabilities of the two independent events to find the combined probability. The probability of both events occurring is (12)×(919)(\frac{1}{2}) \times (\frac{9}{19}).
  5. Find final probability: Perform the multiplication to find the final probability. (12)×(919)=938(\frac{1}{2}) \times (\frac{9}{19}) = \frac{9}{38}.

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