Question 289115: a card is picked from a deck find the odds aginst and the odds in favor of:
a picture card
a seven
a red card
a jack or king
a queen and diamon
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! a card is picked from a deck find the odds aginst and the odds in favor of:
a picture card
a seven
a red card
a jack or king
a queen and diamon
52 cards total
ace is not a picture card --> 4 of those
2 - 10 not picture cards --> 36 of those
that leaves 12 cards (J,Q,K)
12/52 or approx 23.08% are a picture card, 76.92% are not a picture card
odds for: p/(1-p) -->
(12/52)/(1 - (12/52)) = 12/52 / 40/52 = 12/52 * 52/40 = 12/40 = 3/10 or 3:10 for
odds against: (1-p)/p -->
10/3 or 10:3 against
4/52 or approx 7.7% are 7's, 92.3% not a 7
odds for: (4/52)/(48/52) = 4/48 = 1/12 or 1:12 for
odds against: 12/1 or 12:1 against
both diamonds and hearts are red, so 26/52 or 50% are red
both clubs and spades are black, so 26/52 or 50% are black
50% is (26/52)/(26/52) = 1 or 1:1 for and 1:1 against
odds of a jack or a king should be the same as the odds of a 7
1:12 for and 12:1 against
a queen that is a diamond, there is only 1 of these
1/52 or approx 1.9% are this, and 98.1% not
odds for: (1/52)/(51/52) = 1/51 or 1:51 for
odds against: 51:1
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