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Probability is a chance of occurring in an event from total outcomes. With the help of probability, we can predict the happening of an event. The probability range lies between 0 and 1, where 0 means an impossible event, and 1 means a certain event. More probability, more chance of occurring in an event.

Probability of an event P(E)= Number of favourable outcomes/Total outcomes = 0≤P(E)≥1

There are 12 boys and 4 girls in a class. A student is selected at random. Find the probability of selecting a boy?

Number of boys in class P(B) = 12

Number of girls in class P(G) = 4

Total number of students in class P(B+G) = 12+4 = 16

Therefore, the probability of selecting a boy P(E) = Favourable outcome/ Total outcome

=P(selecting a boy)/P(total students)

= P(B)/ P(B+G)

= 12/16

**Sample space-**of the possible outcome of a random trial or experiment.b For e.g., tossing a coin {H,T}**Experiment or trial-**series of action. For e.g., tossing a coin, rolling a die.**Event-**an outcome of an experiment. For e.g., getting a tail after tossing a coin.**Outcome-**possible result of an event. For e.g., P(Tail) is a possible result when a coin is tossed.**Complimentary event-**non-happening of an event. For e.g., A= getting a tail, whereas complement of event A is not A, it is (A’) = not getting tail.**Impossible event-**event that cannot happen. For e.g., getting both head and tail while tossing a coin.

- Sum of probabilities of all possible outcomes is 1.
- For any event A, 0 ≤ P(A) ≤ 1.
- Two events that cannot occur at the same time are called mutually exclusive or disjoint events. Probability of occurring either A or B P(A or B) = P(A) +P(B).
- P(A or B) = P(A) + P(B) – P(A and B) addition rule.
- A and B are Mutually exclusive, then P(A and B) = 0
- A and B are not mutually exclusive, then P(A and B) ≠ 0
- Complement Rule- P(not A) = 1 – P(A)
- P(A or B) = P(event A occurs or event B occurs or both occur)
- P(A and B)= P(both event A occurs and event B occurs)

These are 3 main types of probability:

**Experimental probability:**it is based on the results or observations of an experiment repeated many times. For e.g., a coin is tossed 20 times and got tails 5 times then the experimental probability of getting a tail is-**Theoretical probability:**it is based on the reasoning and expectation of happening something. For e.g., a coin tossed, the probability of getting head is-**Axiomatic probability:**it is a set of rules which applies to all types of probability. And these axioms or rules set by the Kolmogorov and are known as Kolmogorov’s three axioms. For e.g., on tossing a coin, the probability of getting head is ½ and tail is ½. Therefore to be an axiomatic probability should satisfy following conditions-- P(E)≥0 (probability of an event is greater than or equal to 0.
- P(S) = 1 (probability of sample space is equal to one)

P(E)= No.of time event occurs/Total number of experiments = 5/20

P(E)= Count of a favourable outcome/Total no. of a possible outcome

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Probability is a chance of occurring in an event from total outcomes. Get excellent services from our Probability Probability Distributions help experts learn more about its concept. Our Expert Tutors are accessible 24*7 for your help.

- Poisson distribution
- Applied probability
- Statistical dispersion
- Binomial distribution
- Law of total Probabilities
- Probability mass function
- Discrete distribution
- Normal distribution
- Tree and Venn diagrams
- Central limit theorem
- Confidence intervals
- Chi-square distribution
- Random variable
- F distribution
- One way ANOVA
- Outliers
- Sampling
- Data collection experiment
- Uniform distribution
- Exponential distribution
- Types of events
- Probabilities sampling

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