00:01
We are given this problem today from a deck of cards, six cards are chosen at random.
00:35
And to find probability that at least five out of six cards are read.
01:04
So this is the given problem.
01:07
Now let us see how we can solve this.
01:13
Now there are four suits in a deck of 52 cards.
01:35
13 fades which are black, 13 cards which are red, 13 clubs which are black, 13 clubs which are black and 13 diamonds which are red.
02:15
Therefore, there are 26 black and 26 red cards in a, now we have to choose in such a way that at least five of the cards are red.
02:46
So, total number of red cards, 13 plus 13, 26.
03:11
Total number of black cards similarly 13 plus 13 equal to 26 so red or black are evenly distributed now what is the total number of exhaustive cases total number of exhaustive cases we can choose six cards from a deck of 52 cards in 52 c6 ways now what are the number of favorable cases? at least five cards.
04:03
So there must be five or six red cards.
04:09
So how can you choose? first, let us consider five cards.
04:13
How can you choose five cuts? five red cards can be chosen in, there are 26 red cuts.
04:32
So 26, see, five ways.
04:37
And the remaining black card, only one black card can be chosen.
05:06
So there are 26 black cards, only one black card can be chosen in, so 26 ways.
05:17
Therefore, total number of ways that 5 red and 1 black can be chosen equals, 26c5 times 26 ways...