One card is missing in a pack of 52 playing cards. If two cards are drawn randomly from the remaining cards at a time and are found to be spades, then the probability that the missing card is not a spade is

Step-by-step solution

Let E ₁= Event of choosing a spade card E ₂= Event of choosing a card which is not spade Let A denote the lost card. P ( E ₁ )= 13 52 = 1 4 aligned & P (E₂ )= 39 52 = 3 4 & P ( A E₁ )= ¹² C₂ ⁵¹ C₂ = 22 425 & P ( A E₂ )= ¹³ C₂ ⁵¹ C₂ = 26 425 aligned By using Baye's theorem, P ( E₂ A )= P (E₂ ) P ( A E₂ ) P (E₁ ) P ( A E₁ )+P (E₂ ) P ( A E₂ ) aligned & = 3 4 26 425 1 4 22 425 + 3 4 26 425 & = 3 26 22+3 26 = 39 50 aligned