Important Definitions & Formulas: Probability

# Important Definitions & Formulas: Probability | Mathematics (Maths) Class 10 PDF Download

 Table of contents Probability Sample Space of Coin Toss Sample Space of Throwing a Die Geometric Probability Probability while Playing Cards

## Probability

• q(not happening) = 1 - p

## Sample Space of Coin Toss

• When a coin is tossed, S = {H, T}
• When two coins are tossed simultaneously = {HH, HT, TH, TT}
• When three coins are tossed simultaneously = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

## Sample Space of Throwing a Die

• When a die is thrown once = {1, 2, 3, 4, 5, 6}
• When two dice are thrown simultaneously
=> {(1,1), (1,2), (1,3), ...., (1,6)
(2,1), (2,2), (2,3), ...., (2,6)
(3,1), (3,2), (3,3), ...., (3,6)
(4,1), (4,2), (4,3), ...., (4,6)
(5,1), (5,2), (5,3), ...., (5,6)
(6,1), (6,2), (6,3), ...., (6,6)}

## Geometric Probability

If the total number of outcomes of a trial in a random experiment is infinite, then the definition of probability is not sufficient to find the probability of an event, in such cases, the definition of probability is modified and the probability so obtained is called geometric probability. The geometric probability p of an event is given by:

Note: Measure means Length, Area or Volume of the region etc.

## Probability while Playing Cards

Playing cards consists of 52 cards which are divided into four suits of 13 cards each. Each suit consists of one king, one queen, one jack, one ace and nine other cards numbered from 2 to 10. The four suits are named spadeclub heart and diamond (♦).

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## FAQs on Important Definitions & Formulas: Probability - Mathematics (Maths) Class 10

 1. What is the sample space of a coin toss?
The sample space of a coin toss refers to the set of all possible outcomes of the coin toss. In this case, the sample space would consist of two outcomes: heads and tails.
 2. What is the sample space of throwing a die?
The sample space of throwing a die refers to the set of all possible outcomes of the die roll. In this case, the sample space would consist of six outcomes: the numbers 1, 2, 3, 4, 5, and 6.
 3. What is geometric probability?
Geometric probability is a type of probability that is used when the sample space consists of geometric figures. It involves finding the ratio of the desired outcome to the total possible outcomes within the geometric figure.
 4. What are some important definitions and formulas in probability?
Some important definitions and formulas in probability include: - Sample Space: The set of all possible outcomes of an experiment. - Event: A subset of the sample space. - Probability of an Event: The likelihood of an event occurring, represented as a number between 0 and 1. - Complementary Event: The event that an event does not occur. - Probability of Complementary Event: 1 minus the probability of the event. - Addition Rule: The probability of the union of two events is equal to the sum of their individual probabilities minus the probability of their intersection. - Multiplication Rule: The probability of the intersection of two independent events is equal to the product of their individual probabilities. - Conditional Probability: The probability of an event occurring given that another event has already occurred. - Bayes' Theorem: A formula used to update the probability of an event based on new information.
 5. What is the probability while playing cards?
The probability while playing cards refers to the likelihood of certain events occurring in a card game. This can include calculating the probability of getting a specific hand (such as a flush or a straight) or the probability of drawing a certain card from a deck. The calculation of probabilities in card games often involves understanding the concept of combinations and permutations.

## Mathematics (Maths) Class 10

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