Today is our topic of discussion Concept of Probability.
Concept of Probability
In our everyday life we frequently use the word ‘probability? For example, the probability of Jaadob passing the SSC examination this year is really poor, the probability of Bangladesh winning the Asia cup is high, the probability of the temperature rising tomorrow is high, the probability of raining today is very thin etc.
Therefore, we talk about probability only when there is a doubt about an event occurring. And the possibility of the event occurring also depends on the magnitude of non-occurrence. But this procedure can not give any numerical value. In this chapter, we will know about different formulas and procedures for assigning a numerical value to the probability of the occurrence of an event, and we will also be able to describe certain events, impossible events and possible events after studying this chapter. After studying this chapter, students will be able to –
- explain the concept of probability;
- describe certain events, impossible events and possible events by giving daily-life examples;
- describe the consequences of repetition of an event;
- find the probability of an event happening repeatedly; solve simple and
- real-life problems regarding probability.
Basic Concepts Related to Probability
Random Experiment:
A random experiment is where you know all possible outcomes of the experiment, but you can not say the exact outcome of a certain attempt in this experiment. For example, we know all the outcomes of throwing a dice, but we can not exactly tell which outcome will occur before throwing the dice. So the experiment of throwing a dice is a random experiment.
Event:
An outcome or a combination of outcomes of an experiment is called an event. For example, getting 3 after throwing a dice is an event. Again, getting an even number in this regard is also an event.
Equally Likely Events:
If the possibilities of the outcomes of a random
experiment occurring are same, which means no outcome is more or less likely to happen than any other outcome, the possible outcomes are called equally likely events. For example, the occurrence of a head or a tail in the tossing of a coin are equally likely events, unless the coin is defective or biased in some way. Therefore, getting head and tail are equally likely events.
Mutually Exclusive Events:
Two or more possible outcomes of a random experiment are called mutually exclusive event if the occurrence of one of those events precludes the possibility of the other events. For example, in the tossing
of a coin, the occurrence of a head and a tail are mutually exclusive events sinceif head occurs then tail can not occur and vice versa. That means head and tail can not occur at the same time.
Favourable Outcomes:
The outcome of interest of an event in an experiment is called favourable outcome. The number of favourable outcomes of getting an odd number on throwing a dice is 3.
Sample Space and Sample Point:
The set of all possible outcomes of a random experiment is called the sample space. The tossing of a coin has two possible outcomes: Head and Tail. If the result of this experiment is expressed as S, we can write S = {H, T}. So in this case the sample space is S = {H, T}. Suppose two coins are tossed simultaneously. Then the sample space is S = {HH, HT, TH, TT}. Every element of a sample space is called a sample point. The experiment of throwing a dice once has the sample space S {H,T}, and = here each of H, T is a sample point.
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