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How to Calculate Probabilities

- by R. Totten - (C)2005

In everyday conversations we may be satisfied merely to speak of how "likely" or "unlikely" an event might be, however, when discussing some topics it is helpful to be more precise by using numbers to express the chances, and perhaps also to convey how one comes up with those numbers.

The probability that a certain outcome may occur, can have any value between 0 (impossible) and 1 (certain). It may be a fraction, a decimal or a percentage. For instance, the probability of "one chance out of 100" is also expressed by .01 which equals the fraction 1/100.

When different outcomes of an event are equally likely to happen you can use a formula to calculate the probability of a specific outcome:

 Probability of an outcome = number of ways that outcome can happen total number of possible outcomes

For example, when you flip a coin, there are two equally possible outcomes --heads or tails-- and the chance that you will flip tails, is .5 ...or one chance out of two.

Or, for example, when you roll a fair dice, there are 6 equally possible outcomes: 1, 2, 3, 4, 5 and 6. --So, the chance that one roll of the dice will turn up the number 4, is 1/6 ...or one chance out of 6.

To go a bit further --out of the 6 possible outcomes, there are three ways to get an even number on the dice (2, 4 or 6), so the probability of getting an even number is calculated as follows:

 Probability of getting an even number = 3 6 = 1 2 = 0.5 or 50%

Similarly, you can see that the chance of drawing the Ace of spades out of a shuffled pack of 52 cards (on any single given draw), is one chance out of 52 ---however, the chance of drawing any one of the 4 Aces, is 4 chances out of 52 --which equals one chance out of 13.

EVENTS IN SUCCESSION

The probability that independent events will happen in succession, is the PRODUCT of those events.

For example, while the probability that one toss of a coin will turn up heads, is 1/2 (or one chance out of two) --the probability that two tosses of a coin will produce two heads in a row, is 1/2 X 1/2 = 1/4 ...or one chance out of 4.

Taking the example further, the probability that three tosses of the coin will produce three heads in a row, is the product of those three independent events, or 1/2 X 1/2 X 1/2 = 1/8 ...or one chance out of eight.

Applying this principle to the shuffled deck of 52 cards, the probability of drawing the Ace of Spades two times in a row,
is 1/52 X 1/52 = 1/2704 ...or one chance out of 2704,

...HOWEVER...

the probability of drawing any one of the 4 Aces on 2 separate draws from a shuffled deck of 52 cards,
is 4/52 X 4/52 = 16/2704 ...or one chance out of 169.

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