two cards are drawn without replacement from a 52 deck of cards. what ae the odds against drawing a club and a diamond? can you walk me through this? thank you

Why don't you attempt the problem first? I would be happy to critique your work.

Hint: keep in mind that while probability is the good/total, odds are the good/bad.

D) 13 : 191

I'm not quite sure where you got 191.

Assuming you mean drawing a club and a diamond in that order:

the odds against drawing a club first are 39/13;
the odds against drawing a diamond next (without replacement) are 38:13;

So the odds against drawing a club and then a diamond are 39*38 : 13*13, or 114:13

If, however, you meant drawing a club and a diamond, in no particular order, then you must consider the odds against drawing a diamond first and then a club.

Those odds are the same as the odds against drawing a club first and then a diamond (as there are only 2 cards drawn), so just double the answer found above.

The odds against drawing a club and a diamond in no particular order are 114:26 or 57:13

Well you see that answer does not match with one of the multiple choice rather it's and we know that it's not D so I'm assuming it's A then.

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

thank you for your help. The answer is A. Right?

Of course! Let's break down the problem step by step.

First, we need to determine the total number of possible outcomes when drawing two cards without replacement from a standard 52-card deck.

When drawing the first card, there are 52 options to choose from. After selecting the first card, there are 51 cards remaining in the deck. Therefore, the total number of possible outcomes is (52 * 51) = 2652.

Next, we need to determine the number of favorable outcomes, which represent the scenarios where we draw a club and a diamond.

There are 13 clubs and 13 diamonds in the deck. When drawing the first card, we have 13 club options. After selecting the first card, there are 13 diamonds remaining in the deck to choose from.

Therefore, the number of favorable outcomes is (13 * 13) = 169.

Now, we can calculate the odds against drawing a club and a diamond. To do this, we divide the number of unfavorable outcomes by the number of favorable outcomes.

The number of unfavorable outcomes is equal to the total number of possible outcomes minus the number of favorable outcomes. So, (2652 - 169) = 2483.

Finally, we can express the odds against drawing a club and a diamond as a ratio or a fraction. The odds ratio is given by the number of unfavorable outcomes divided by the number of favorable outcomes, which in this case is 2483/169. This can also be expressed as a fraction, where the numerator (2483) represents the number of unfavorable outcomes and the denominator (169) represents the number of favorable outcomes.

Therefore, the odds against drawing a club and a diamond would be 2483 to 169, or alternatively, as a fraction approximately equal to 14.69 to 1.

I hope this explanation helps you understand how to calculate the odds against drawing specific cards from a deck! Let me know if there's anything else I can assist you with.