Q1)A party of n persons sit at a round table then odds against 2 persons sit together will be: Q2) a pack of playing cards was found to contain only 51 cards. If the first 13 cards which are examined are all red, then the probability that the missing card is black is:

hi varsha,

we hav to arrange n persons along  d round table.

toatal ways of arranging them round d table = (n-1)!

now we wish 2 persons come together den we can do one thing dat we combine both of dem as a single person n after dat we hav (n-1) persons n

total ways of arranging dem = (n-1-1)! * 2! [ as dose 2 persons can be arranged demselves]

                                         = (n-2)! * 2

probability of this event = (n-2)! * 2 / (n-1)! = 2/ (n-1)

n odd against dis event = 1-2/(n-1) = (n-3)/(n-1).

hi varsha,

since out of 51 cards we checked 13 n all of dem r red, dat means out of d 38 cards, either of d two case may occur, 1.) one red card is missing or 2.) one black is missing

in 1st case, der wud be 26 blacks n 12 red

in 2nd case., der wud be 25 blacks n 13red

in total of 39 cards , der r 38 available n 1 is missing ,

required p = when black is missing/either red or black is missing

p (black is missing) = 26 c 25 * 13 c 13 /( 26 c 25 * 13c 13 + 26c16 * 13 c 12) = dis will give u

p = 2/3