Question

7 cards are drawn simultaneously from a standard deck of 52 cards.what is the probability that at least 6 of cards drawn are red?

Answer 1

Total number of possible outcomes =52
favourable number of outcomes= 13+13=26
probability of getting at least 6 red cards= 26upon52

Answer 2

`((26c6*26c1)+(26c7*26c0))/(52c7)` probability that at least 6 cards drawn are red

Explanation:

Total cards drawn = 7

total cards on deck = 52

Total possibility from 52 cards =
`52_(c)` = 133784560

Note : in a standard card deck (52) there are : 13 spades, 13 clubs, 13 hearts and 13 diamonds and they contain king,queen, jack and ace , 2,3,4,5,6,7,8,9 and 10

Note : there are only two colors ( red and black ) : spades and clubs are black while hearts and diamonds are red

probability that at least out of 7 cards drawn 6 cards are red

P ( red ≥ 6 ) = ( 6 red , 1 black ) , ( 7 red , 0 black )

= 26c
`_(6)` * 26c
`_(1)` + 26c
`_(7)` * 26c
`_(0)`

probability =
`((26c6*26c1)+(26c7*26c0))/(52c7)`