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Probability Formulas

The likelihood of an event happening is probability. A fine day during rainy season may have the probability to rain on a particular day or not to rain. We can say that in both the situations each outcome is equally likely. Then in this type of situation, we can use the formula to find the chances of happening of an event.
A chance of prediction is probability – when we are betting on happening of an event then the chances, let’s say, are said to be “x” and at the same time betting on not happening of an event is just the opposite of the variable, that is, “1-x”. Similarly if the probability of an event occurring is “a” and an independent probability is “b”, then the probability of both the event occurring is “ab”
The formula of probability of an event is:

Probability of an event

By favourable outcome we mean that the outcome of interest. One should not confuse the word “favourable outcome” with desirable outcome. In some of the requirements, losing in a certain test or occurrence of an undesirable outcome can be a favourable event for the experiments run.

Now let’s see an example: What is the probability that a card taken from a deck of cards, which by the way has 52 cards, is an Ace? Since we know that the number of aces that a deck of card contains is four, the number of favourable outcome will be four. Now, by looking at the formula we come to the conclusion that the probability of finding an ace from a deck would be =
P(Ace) = Number of favourable outcome / Total number of favourable outcomes)

P(Ace) = 4/52
= 1/13

So we can say that the probability is 1/13.

When we talk about independent events then the probability of event A occurring is just as equal even if event B is occurring or not. Suppose a coin is tossed twice. The probability if the head is coming up on the second toss is ½ even if head came in the first toss. These events are independent. It is the same way when we say “It will rain tomorrow in Delhi” and “It will rain tomorrow in Mumbai” since these two events are not related. We call these events independent because it is possible that it might rain in Delhi when it is not raining in Mumbai.

In formulas, representing the probability of independent individual event happening is –

probability

So, In our coin example above, the probability that heads with come up both time is :

½ X ½ = ¼

Now let’s solve some more examples:

 

Solved Examples

Question 1: Calculate the probability of getting an odd number if a dice is rolled?

Solution:

Sample space(S) if a die is rolled = {1, 2, 3, 4, 5, 6}
Let “E” be the event of getting an odd number, E = {1, 3, 5}
So, the Probability of getting an odd number P(E) = $\frac{Number of outcomes favorable}{Total number of outcomes}$ = $\frac{n(E)}{n(S)}$ = $\frac{3}{6}$ = $\frac{1}{2}$
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