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## Probability Question

One card selected randomly from deck. Find odds against drawing a spade greater than 2 and less than 9

What the other tutors gave was probability. Odds for an event is defined as the ratio of the probability for the event to the probability against it.

In your case, the event E consists of picking one of the six cards 3S, 4S, 5S, 6S, 7S, 8S (S = Spades).

There are 6 ways for E to happen, and 46 ways for it not to happen. so the odds against E is

46:6 = 23:3

Out of a deck of cards (which always has 52 cards) there are four suits, so 1/4 of all the cards will be of the suit spades. 1/4 of 52 is 13 cards. The thirteen cards will be numerical cards from 2-10 and the face cards (King, Queen, Jack and Ace). So the cards that would be a spade greater than 2 and less than 9 (non-inclusive) would be these six cards: 3,4,5,6,7 and 8. The odds of drawing one of those cards would be 6/52 or 3/26 when you simplify. The odds against drawing one of those six would be 46/52 or 23/26 when simplified. Hope this is helpful!

I am assuming that this is a standard 52 card deck without the jokers.

The cards that are greater than 2 and less than 9 are:  3, 4, 5, 6, 7, and 8, for a total of 6 possible cards.

Since there are 6 cards that I am trying to draw out of 52 possibilities, my odds are:

6/52

This reduces to 3/26.