Laws of Probability




Laws of ProbabilityThis is an example of what is known as an ill posed question. That is to state, we cannot provide a mathematical answer until we understand all the assumptions.

If we assume that each person's birthday is equally likely to be any of the 365 days of the yr and that one individual's birthday has no impact on anybody else's, then the answer is that simply 23 people suffice.

How to do Probability

Probability is a kind of ratio in which we compare the number of times an outcome can take place compared to all possible outcomes.

Example:

What is the probability to obtain a 6 whenever you roll a die?

A die provides 6 sides, 1 side include the number 6 that provide us 1 wanted outcome in 6 possible outcomes.

Independent occasions: Two occasions are independent once the outcome of the initial event does not influence the result of the second event. When we do the probability of 2 independent occasions we multiply the probability of the very first event by the probability of the 2nd event.

P(X and Y) = P(X) . P(Y)

Probability Problems and Solutions

In what follows, S is actually the sample space of the experiment in question and E is the occasion of interest. n(S) is the number of components in the sample space S and n(E) is the number of components in the event E.

Question 1: A die is rolled, locate the probability that an even number is obtained.

Solution to Question 1: Let us very first write the sample space S of the experiment.

S = 1,2,3,4,5,6

Let E be the occasion an even number is obtained and write it down.

E = 2,4,6

We now utilize the formula of the classical probability.

P(E) = n(E) / n(S) = 3 / 6 = 1 / 2

Question 2: Two coins are tossed, find the probability that 2 heads are obtained.

Note: Every coin has 2 possible outcomes T (Tails) and H (heads).

Solution to Question 2:

The sample space S is provided by.

S = (H,T),(H,H),(T,H),(T,T)

Let E be the event "two heads are obtained".

E = (H,H)

We utilize the formula of the classical probability.

P(E) = n(E) / n(S) = 1 / 4 



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