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What is the probability of getting a number less than 2 on rolling a dice?

  • Last Updated : 18 Oct, 2021

In daily life, usually the word ‘probably’ is used when people are not sure about certain things. For example, Probably, India may win the match today. There may be a chance that India may win or lose or maybe the match is a tie. This type of statement leads to the uncertainty of the event. The word Probability is formed from the word word ‘probably’, which means that when people are not sure about an event is happens or not. People have a proper method to find out the probability which will be discussed in this article. 

Terms used in Probability

  • Random Experiment: In the random experiment, we can not predict the result in advance. For example, if we toss a coin we can not predict that the head will appear, the tail also may appear.
  • Event: Collection of some outcome of an experiment is known as an event.
  • Sample Space: It is the collection of all possible outcomes. Suppose a dice is rolled out then the possible outcome is 1, 2, 3, 4, 5, or 6. It is denoted by S. S = (1,  2, 3, 4, 5, 6)
  • Rolling of Dice: A dice is a solid cube shape. It has 6 square faces. The six faces are marked by 1, 2, 3, 4, 5, 6 dots. When a fair dice is rolled, then the total possible outcome is 1, 2, 3, 4, 5, or 6. So all these numbers are known as sample space.

Probability 

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The probability of an event is defined as the ratio of favorable outcomes to the sample space or total outcomes. We represent it by ‘P’.



Probability of an event (P) = ( Number of Favourable outcomes) / (Total number possible outcomes)

What is the probability of getting a number less than 2 on rolling a dice?

Solution:

Concept: To solve the given problem, follow the steps given below.

Step 1: First of all find out all possible outcomes of the given event. Represent it by S.

Step 2: Specify the number of favorable outcomes.

Step 3: Use the formula, Probability of an event = (Favorable outcomes) / (Total number of possible outcomes)

Step 4: Simplify and get the final answer.

When a dice is rolled, all possible outcomes are 1, 2, 3, 4, 5, 6.



We call it as sample space, S = (1, 2, 3, 4, 5, 6)

So total number of possible outcomes = 6

Favorable outcome (Required outcome) = 1

(Only 1 is smaller than 2, remaining number is greater than 2 so we will not consider them as favorable outcomes.)

So total number of favorable outcomes = 1

Probability = (Total number of favorable outcomes)/(Total number of possible outcomes)

Probability = 1/6 

So, the probability of the given statement is 1/6.

Similar Questions

Question 1: What is the probability of rolling a number greater than 4 on a dice? 

Solution:

When a dice is rolled, all possible outcomes are 1, 2, 3, 4, 5, 6.

S = (1, 2, 3, 4, 5, 6)

Number of possible outcomes, n(S) = 6

Favorable outcomes = (5, 6)

(Only 5 and 6 is greater than 4, so these two will be favorable cases)

Number of favorable outcomes, n(F) = 2

Probability = (Number of favorable outcomes)/(Number of total outcomes)

Probability = 2/6

 =1/3

So, the probability of the given statement is 1/3.



Question 2: What is the probability of rolling an odd number on a dice?

Solution

 When a dice is rolled, all possible outcomes are 1, 2, 3, 4, 5, 6.

 S = (1, 2, 3, 4, 5, 6) 

 Number of possible outcomes, n(S) = 6

 Favorable outcomes = (1, 3, 5)

 (Only 1, 3, 5 are the odd number obtained when a dice is rolled)

 Total number of favorable outcomes, n(F) = 3

 Probability = (Number of favorable outcomes)/(Number of total outcomes)

 Probability = 3/6 

 = 1/2

 So, the required probability is 1/2. 

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