I'm really stuck in this question can someone please help me out in this one.

Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What are the odds against drawing a club and a diamond?

first find the prob of getting a club and a diamond.

DC --> (13/52)*(13/51) = 169/2652 = 13/204
CD --> (13/52)*(13/51) = 13/204

so prob of club and diamond = 13/102

OR prob of club and diamond = C(13,1)*C(13/1)/C(52/2) = 13/102

so prob of NOT gettting a club and diamond = 89

so the odds AGAINST a club and diamond
= 89:13

Reiny this are my mult. choice that I need to choose from I'm studying for my exam for next week.

A) 204 : 13
B) 191 : 13
C) 13 : 204
D) 13 : 191

i have worked it I got the answer like you I guess I just need to go with what you and I got right?

odds in favour of some event

= (prob of that event happening):(prob of that event not happening)

since the prob of a club and a diamond is less than the prob of NOT a club and a diamond, we can automatically eliminate choices C and D

choice B would be correct if the wording had been ...
"What are the odds against drawing a club and a diamond in that order ?"

but from the given wording I concluded it could be club-dimaond OR dimaond-club.

The wording should have been more explicit.

BTW, my line of :
so prob of NOT gettting a club and diamond = 89

should have been "
so prob of NOT gettting a club and diamond = 89/102
but I think you figured that out already.

To find the odds against drawing a club and a diamond, we need to calculate the number of unfavorable outcomes and divide it by the number of favorable outcomes.

First, let's determine the total number of possible outcomes. When two cards are drawn from a deck of 52 playing cards without replacement, the first card can be any of the 52 cards, and the second card can be any of the remaining 51 cards. Therefore, the total number of possible outcomes is 52 * 51.

Next, let's find the number of favorable outcomes, which is the number of ways we can draw one club and one diamond. There are 13 clubs and 13 diamonds in a deck, so the number of favorable outcomes is 13 * 13.

Finally, we can calculate the odds against drawing a club and a diamond by dividing the number of unfavorable outcomes (total - favorable) by the number of favorable outcomes. In this case, the number of unfavorable outcomes is (52 * 51) - (13 * 13).

Now, we can calculate the odds against drawing a club and a diamond:

Odds against = Number of unfavorable outcomes / Number of favorable outcomes

Odds against = [(52 * 51) - (13 * 13)] / (13 * 13)

By simplifying this expression, you can find the odds against drawing a club and a diamond.