SOLUTION: What are the odds that you will pick a 5 from a standard deck of 52 cards? What are the odds of rolling a number greater than 3 on a regular six sided die?

Question 895126: What are the odds that you will pick a 5 from a standard deck of 52 cards?
What are the odds of rolling a number greater than 3 on a regular six sided die?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
odds and probability are different, but related.

odds for equals probability for divided by probability against.

odds against equals probability against divided by probability for.

there are 4 number 5's in the deck.
they are the 5 of clubs, the 5 of spades, the 5 of hearts, and the 5 of diamonds.

the probability of drawing a 5 from the deck is 4/52.
the probability of not drawing a 5 from the deck is 48/52

the odds of drawing a 5 from the deck are 4/52 divided by 48/52 which is equal to 4/52 * 52/48 which is equal to 4/48 which is equal to 1/12 which means 1 to 12.

the odds against drawing a 5 from the deck are 48/52 divided by 4/52 which is equal to 48/51 * 52/4 which is equal to 48/4 which is equal to 12/1 which means 12 to 1.

your odds of drawing a five from the deck are 1 to 12.
your odds against drawing a five from the deck are 12 to 1.

when you roll a die, the probability of getting any number is 1/6.

the probability of rolling a number greater than 3 equals the probability of rolling a 4 or a 5 or a 6 which is equal to 3/6 which is equal to 1/2.

the probability of not rolling a number greater than 3 is also equal to 1/2.

the odds of rolling a number greater than 3 is equal to 1/2 divided by 1/2 which is equal to 1/2 * 2/1 which is equal to 1/1 which means 1 to 1.

the odds of not rolling a number greater than 3 is equal to 1/2 divided by 1/2 which is equal to 1/2 * 2/1 which is equal to 1/1 which means 1 to 1.

the odds are considered even because the odds for is the same as the odds against.

you convert odds to probability by adding the numerator and denominator together and that becomes the denominator of the probability.

example:

4/5 odds becomes 4/9 probability.
the 4 is added to the 5 and that gets you 9 which is the denominator of the probability.

you convert probability to odds by subtracting the numerator from the denominator and that becomes the denominator of the odds.

example:

4/9 probability becomes 4/5 odds.
the 4 is subtracted from the 9 and that gets you 5 which is the denominator of the odds.

here's a reference:

http://www.mathplanet.com/education/pre-algebra/probability-and-statistic/finding-the-odds

note that odds for is equal to the number of chances to succeed divided by the number of chances to fail means the same as the probability of success divided by the probability of failure.

example:

you try 10 times.
you get 2 successes out of 10 tries.
the probability of success = 2/10
the probability of failure = 8/10

the odds of success = probability of success divided by probability of failure.

this is equal to (2/10) / (8/10) which is equal to (2/10) * (10/8) which is equal to (2/8).

the denominator of the probability cancels out in the division and you are left with 2/8.

2/8 is the number of successes divided by the number of failures.

odds of success = probability of success / probability of failure = number of successes / number of failures.

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