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# What is the probability of an even throw on a die?

Module by: Arnold Mwesigye. E-mail the author

The word probability is used to express uncertain events or knowledge, being closely related in meaning to likely, risky, hazardous, and doubtful. Chance,odds, and bet are other words expressing similar notions.

Probabilities are also thought of as numbers in a closed interval from 0 to 1 assigned to "events" whose occurrence or failure to occur is random.

The probability P of some event E , denoted P(E), is defined with respect to a sample space of all possible elementary events.

Probability P(A), assigned to an event A, is defined as the number of possible occurrences in A, as a ratio of the sample space.

Therefore;

P(A) = N(A) / N(S)

To determine the probability of an occurrence we need to define it with respect to a sample space of all possible elementary events.

Example:

If we define the probability of an even throw as the event, E, then;

E = { 2, 4, 6 }

If we define the sample space, S, as the total number of possible throws, then;

S = {1, 2, 3, 4, 5, 6}.

The probability of an even throw on a die is;

P(E) = P(E) / P(S)

P(E) = Number of even throws / Total number of possible throws

P(E) = 3/6 = 1/2.

Exercise:

In a single throw of a die, what is the probability of getting a number greater than four? Answer.

References:

Wikipedia. "Statistical Independence", Wikipedia Foundation Inc, "http://en.wikipedia.org/wiki/Probability", Last accessed 17th February 2006.

Arnold Mwesigye

Petrina Mangala

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