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Tips & Tricks: Probability | Tips & Tricks for Government Exams - Bank Exams PDF Download

Introduction

  • Probability is the section of mathematics, that deals with the results of random events. The word probability means chance or possibility of an outcome. It explains the possibility of a particular event occurring. We often use sentences like - ‘It will probably rain today, ‘he will probably pass the test’, ‘there is very less probability of getting a storm tonight’, and ‘most probably the price of onion will go high again. In all these sentences, we replace words like chance, doubt, maybe, likely, etc., with the word probability.

Tips & Tricks: Probability | Tips & Tricks for Government Exams - Bank Exams

Theory

  • Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event. In such cases, we say that there is a probability of this event to occur or not occur. Probability generally has great applications in games, in business to make probability-based predictions, and also probability has extensive applications in this new area of artificial intelligence.
  • The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes. The value of the probability of an event to happen can lie between 0 and 1 because the favorable number of outcomes can never cross the total number of outcomes. Also, the favorable number of outcomes cannot be negative.

Formula's

  • The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes. The probability formula can be expressed as,
    P(E) = Number of favorable outcomes/Number of total outcomes
    Or,
    P(E) = n(A)/n(S)

where,

  • P(B) is the probability of an event 'B'.
  • n(B) is the number of favorable outcomes of an event 'B'.
  • n(S) is the total number of events occurring in a sample space.

Tricks

  • When we throw a coin on the air, the coin appears either a Head (H) or a Tail (T).
  • A dice is a solid cube having 6 faces, marked as 1, 2, 3, 4, 5, 6 gradually. When we throw a dice the outcome is the number that appears on it’s upper face of the dice.

Solved Examples

Question for Tips & Tricks: Probability
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The probability of two persons of passing the interview are 1/3 and 3/5. Then calculate the probability that only one of them pass the interview ?

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Question for Tips & Tricks: Probability
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Among a group of 5 boys and 6 girls, 4 members is to be selected for an event. Find the probability that at least one boy is selected ?

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Question for Tips & Tricks: Probability
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The probability that the problem will be solved by three persons are 1/2, 1/3 and 1/6. Find the probability that the problem is solved ?

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Question for Tips & Tricks: Probability
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A urn contains 4 red balls, 5 green balls and 6 white balls, If one ball is drawn at random, find the probability that it is neither red nor white ?

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The document Tips & Tricks: Probability | Tips & Tricks for Government Exams - Bank Exams is a part of the Bank Exams Course Tips & Tricks for Government Exams.
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FAQs on Tips & Tricks: Probability - Tips & Tricks for Government Exams - Bank Exams

1. What is probability and how is it calculated?
Ans. Probability is a measure of the likelihood of an event occurring. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
2. What is the difference between theoretical probability and experimental probability?
Ans. Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability, on the other hand, is based on actual observations or experiments and may vary from the theoretical probability.
3. How do you find the probability of two independent events occurring?
Ans. To find the probability of two independent events occurring, you multiply the probabilities of each event. This can be calculated using the formula: P(A and B) = P(A) * P(B).
4. What is the concept of complementary events in probability?
Ans. Complementary events in probability are two events that together encompass all possible outcomes. The probability of either event occurring is equal to 1. For example, if the probability of event A is 0.4, then the probability of event A not occurring (complementary event) is 0.6.
5. How do you calculate the probability of dependent events?
Ans. To calculate the probability of dependent events, you multiply the probability of the first event by the conditional probability of the second event given that the first event has already occurred. This can be calculated using the formula: P(A and B) = P(A) * P(B|A), where P(B|A) denotes the probability of event B given that event A has occurred.
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