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

0.74141

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

=
`(52)/(52)`

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

=
`(51)/(52)`

P(C₃,C₁ ∩ C₂) =
`(50)/(52)`

P(C₄,C₁ ∩ C₂ ∩ C₃) =
`(49)/(52)`

P(C₅,C₁ ∩ C₂ ∩ C₃ ∩ C₄) =
`(48)/(52)`

P(C₆,C₁ ∩ C₂ ∩ C₃ ∩ C₄ ∩ C₅) =
`(47)/(52)`

General multiplication rule

P(A) =P(C₁ ∩ C₂ ∩ C₃ ∩ C₄ ∩ C₅ ∩ C₆)

=
`(52)/(52). (51)/(52). (50)/(52). (49)/(52). (48)/(52) .(47)/(52)`

= 8,808,975 / 11,881,376

= 0.74141