Question

A single card is drawn at random from each of six well-shuffled decks of playing cards. Find the probability that all six cards drawn are different.

Answer 1

Answer:

0.74141

Step-by-step explanation:

There are 52 cards in total

since each card is different,

the probability = number of favorable cards / total number of outcomes

P(C₁) = number of favorable cards / total number of outcomes

     = $\frac{52}{52}$

P(C₂, C₁) = number of favorable cards / total number of outcomes

   = $\frac{51}{52}$

P(C₃,C₁ ∩ C₂) = $\frac{50}{52}$

P(C₄,C₁ ∩ C₂ ∩ C₃) = $\frac{49}{52}$

P(C₅,C₁ ∩ C₂ ∩ C₃ ∩ C₄) = $\frac{48}{52}$

P(C₆,C₁ ∩ C₂ ∩ C₃ ∩ C₄ ∩ C₅) = $\frac{47}{52}$

General multiplication rule

P(A) =P(C₁ ∩ C₂ ∩ C₃ ∩ C₄ ∩ C₅ ∩ C₆)

         = $\frac{52}{52}. \frac{51}{52}. \frac{50}{52}. \frac{49}{52}. \frac{48}{52} .\frac{47}{52}$

         = 8,808,975 / 11,881,376

         = 0.74141