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?
you already posted this question before. type in this same question in the little jiskha search box and you will see what I mean.
To calculate the odds against drawing a club and a diamond, we first need to determine the number of favorable outcomes (cards that meet the specified condition) and the number of total outcomes.
Total Outcomes:
When two cards are drawn without replacement from a deck of 52 playing cards, there are a total of 52 cards for the first draw and 51 cards remaining for the second draw. Therefore, the total number of outcomes is given by 52 multiplied by 51.
Favorable Outcomes:
To determine the number of favorable outcomes, we need to consider two cases separately:
Case 1: Drawing a club and then a diamond.
There are 13 clubs in a deck, so the probability of drawing a club on the first draw is 13/52. After the first draw, there are 51 cards remaining, out of which there are 13 diamonds. Therefore, the probability of drawing a diamond on the second draw is 13/51. To find the total favorable outcomes in this case, we multiply these probabilities: (13/52) * (13/51).
Case 2: Drawing a diamond and then a club.
Similar to the first case, the probability of drawing a diamond on the first draw is 13/52. After the first draw, there are 51 cards remaining, out of which there are 13 clubs. Therefore, the probability of drawing a club on the second draw is 13/51. To find the total favorable outcomes in this case, we multiply these probabilities: (13/52) * (13/51).
Finally, we add the favorable outcomes from both cases:
Favorable Outcomes = (13/52) * (13/51) + (13/52) * (13/51)
To calculate the odds against an event, we divide the number of unfavorable outcomes by the number of favorable outcomes.
Unfavorable Outcomes = Total Outcomes - Favorable Outcomes
Therefore, the odds against drawing a club and a diamond can be calculated as:
Odds Against = Unfavorable Outcomes / Favorable Outcomes
I hope the explanation helps you understand how to calculate the odds against this event.