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# Compound Events

A compound event is an event that has more than one possible outcomes. We have already seen the simple events and other types of events. In a compound event, an experiment gives more than one possible outcomes. These outcomes may have different probabilities but they are all equally possible. Here we will see what we mean by this and many examples that are relevant to the banking exams and similar exams. Let us begin with defining the compound events.

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## Compound Events

An event is an occurrence that can be determined by a given level of certainty. For example, when we say that the probability of an event happening is high or low, we are stating the fact that the event may or may not happen in a given way. The ways in which an event can happen are what we call the outcomes of an event. Many of the events that you see around you can have different outcomes. Such events are known as the compound events.

Here many people land up in confusion. All the events that happen around you will have a unique outcome in a given time. For example, it will either rain or not rain but it can only be one of the two. It can’t be both. So isn’t no event a compound event? The answer is in the fact that when we define the compound event, we count the number of possible outcomes. The possible outcomes may be many. In fact, in most of the experiments, they are many. For example, it may rain is one possible outcome, it may not is another, it might snow and so on. So we may have many possible outcomes and those events will form a compound event.

You may similarly try and find many examples around you of compound events. Now the question is how do we find the probability of a compound event? We don’t, rather we find the probability of the various outcomes of the compound event. The total probability of all the outcomes of a compound event is always = 1. If a compound event has N possible outcomes, then the probability of m-th outcome, where m < N is =

P (m) = m/N. As we can see this ratio will always be less than 1. Let us see some examples that will allow us to understand the concept in detail.

## Some Solved Examples

Example 1: First, let us see if we can identify what a compound event is or not. Consider two dice one of which has 1 written on all of its 6 faces and other that has either 1 or 2 on its faces. In the second one, half of the faces are marked with odd numbers and half with even. If A is the probability of getting 1 upon rolling the first dice and B is the probability of getting 2 upon rolling the second dice, then:

A) A is greater than B.

B) B is a simple event while as A is a compound event.

C) A is a compound event while B is a simple event.

D) A is less than B.

Answer: As we saw, the possible outcomes of an event determine if it is a compound event or not. In the first case or case A, one might argue that either of the six faces can turn up so it is a compound event. But because all of the six faces of the dice are same, it is a simple event and its probability will be maximum.

Now B has two possible outcomes. Either the dice can turn up a 1 or a 2. Thus the probability of getting a 2 will be 1/2 which is less than the probability of getting a 1 in the first dice. So A will always be greater than B. Therefore, the correct option here is A) A is greater than B.

Example 2: There is a basket on a basketball court. A basketball player, who never misses takes a random shot at the basket. What is the probability that the ball will go into the basket?

A) 1                B) 0.9                  C) 0.7                D) 0.5

Answer: One might be tempted by a callous look to select the option A) but that would be incorrect. For calculating the correct value of the probability, one must realise that history of any event doesn’t determine the present probability. Moreover, since the question clearly says that the basketball player takes a random shot, the event can happen in two ways. he can either score or he can miss. So the probability of scoring or the probability that the ball will go into the basket is = (odds in favour)/(Total odds) = 1/2.

Hence the answer is D) 0.5

## Practice Questions

Q 1:  What is the probability that a dice with 12 faces returns a value = 9 if each face has a number starting from 0.

A) 0                B) 1/9                C) 1/11                D) 1/12

Ans: D) 1/12

Q 2: A couple decides to start a family and adopt a kid. After a year, they adopt another kid. What is the probability that the first kid is a girl?

A) 1/5              B) 1/4               C) 1/2                 D) 1/4

Ans: A) 1/2

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