Question

A deck consists of 72 cards with 9 suits labelled ? to ? and numbered ranks from 1 to 8. That is, there are 8 cards of each suit and 9 cards of each rank. What is the probability of it being suit C or having rank 6?

Answer 1

Solution:

Given: A deck consists of 72 cards with 9 suits labelled ? to ? and numbered ranks from 1 to 8. That is, there are 8 cards of each suit and 9 cards of each rank.

That is Suits are: A , B, C, D, E, F, G, H, I

Each suit has 8 ranks from 1 to 8.

We have to find:

P( it being suit C or having rank 6) = .........?

Let C = Suit C and 6 = Rank 6

Thus

P( C or 6 ) = ..........?

Using addition rule of probability:

P(C or 6) = P( C) + P( 6) - P( C and 6)

P(C) = Total cards of C / Total cards in Deck

P(C) = 8 / 72

( Since there are 8 ranks of suit C)

P(6) = Total cards of 6 / Total cards in Deck

P(6) = 9 / 72

( since there 9 suits each have card of rank 6)

and

P(C and 6) = 1 / 72

( since there is only one card which is of suit C and Rank 6)

Thus

P(C or 6) = P( C) + P( 6) - P( C and 6)

P(C or 6) = 8 /72 + 9/72 - 1/72

P(C or 6) = ( 8 + 9 - 1 ) / 72

P(C or 6) = 16 / 72

P(C or 6) = 2 / 9

P(C or 6) = 0.222222

P(C or 6) = 0.2222

Thus  the probability of it being suit C or having rank 6 is :  2/9 or 0.2222