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A card is lost from a pack of 52 playing cards. From the remainder of the pack, one card is drawn and is found to be spade. The probability that the missing card is a spade is

Options

  1. A5 1 7
  2. B4 1 7
  3. C3 1 7
  4. D2 1 7

Correct answer

B. 4 1 7

Step-by-step solution

Let A and B are the events that card lost is spade and card drawn is a spade. P A = 1 4 , P A ¯ = 3 4 P B / A = 1 2 5 1 , P B / A ¯ = 1 3 5 1 P A / B = P A · P B / A P A · P B / A + P A ¯ P B / A ¯ = 1 4 · 1 2 5 1 1 4 · 1 2 5 1 + 3 4 · 1 3 5 1 = 1 2 5 1 = 4 1 7

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