Which answer, if any, is correct to:
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? My options are 13:204; 204:13, 13;191; or 191:13
I had two different people help me and here are the two different answers.
13/52*13/51= 169/2652= 13204 = 204:13
The other way was, but doesn't make sense is: P(club and diamond) = (13/52)(13/51)
P(not drawing a club and a diamond) = 1 - ( /(52*51)) = (52*51-13 )/(52*51)
odds against = P(against)/P(for) = (52*51- )/ = 2483:169= 191:13
prob(club and diamond) = 2(13/52)(13/51) = 13/102
prob(not club and diamond) = 89/102
odds against a club and diamond = 89 : 13
Now I have four different answers.
It would be,
there are 13 diamonds and 13 clubs.
because 13/52 is 1/4 which is how many cards of diamonds, clubs, hearts, or spades each have.
SO, if a person draws one card (we're assuming this is a club) which could be 13/52 because there are 13 total clubs, then there would be 1 less card from the 52, so the next fraction would be 3/51 because one card has been tooken away.
To find the odds against drawing a club and a diamond, we need to calculate the probability of not drawing a club and a diamond and then express it as odds.
The correct approach is to calculate the probability of not drawing a club and a diamond. Let's break down the calculation:
The probability of drawing a club on the first draw is 13/52 since there are 13 clubs in a deck of 52 cards.
After the first draw, there are 51 cards remaining, out of which 13 are diamonds.
So, the probability of drawing a diamond on the second draw, given that the first draw was a club, is 13/51.
To calculate the probability of not drawing a club and a diamond, we multiply the probabilities of these two independent events:
P(not drawing a club and a diamond) = (39/52) * (38/51) = 1482/2652 = 247/441
Now, to express this probability as odds against, we divide the probability of not drawing a club and a diamond by the probability of drawing a club and a diamond:
Odds Against = P(against) / P(for) = (247/441) / (13/2652) = (247/441) * (2652/13) = 2483:169
Therefore, the correct answer is 2483:169, which is the same as 191:13.