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

Answer:

$\frac{(26c6*26c1)+(26c7*26c0)}{52c7}$ probability that at least 6 cards drawn are red

Step-by-step 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 = $\frac{(26c6*26c1)+(26c7*26c0)}{52c7}$

Answer 2

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