A die is rolled. what is the probability of getting a prime number or an odd number?

Solution:

We use the basic formula of probability to solve the problem.

Number of outcomes on throwing a die is (1, 2, 3, 4, 5, 6) = 6

Number of prime numbers on dice are 1, 3 and 5 = 3

(i) Probability of getting a prime number = Number of prime numbers/total number of outcomes

= 3/6 = 1/2

(ii) Numbers lying between 2 and 6 are 3, 4, 5 = 3

Probability of getting a number lying between 2 and 6 = Number lying between 2 and 6/total number of outcomes

= 3/6 = 1/2

(iii) Total number of odd numbers are 1, 3 and 5 = 3

Probability of getting a odd number = Number of odd numbers/total number of outcomes

= 3/6 = 1/2

☛ Check: NCERT Solutions Class 10 Maths Chapter 15

Video Solution:

A die is thrown once. Find the probability of getting (i) a prime number; (ii) a number lying between 2 and 6; (iii) an odd number.

NCERT Solutions for Class 10 Maths Chapter 15 Exercise 15.1 Question 13

Summary:

If a die is thrown once, then the probability of getting (i) a prime number, (ii) a number lying between 2 and 6, and (iii) an odd number are 1/2, 1/2, and 1/2 respectively.

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Answer

Verified

Hint: In this question it is given that if a die rolled once, then we have to find the probability of getting an odd prime number. So for this we need to know the expression of probability, which is,
Probability(P)=$$\dfrac{\text{Number of favourable outcomes} }{\text{Total number of outcomes} }$$.....(1)
So from the given data we have to find the all possible outcomes and the number of possible outcomes.Complete step-by-step solution:
As we know that a die is a six-sided cube with the numbers 1-6 placed on the faces.
So from here we can say that if we throw a die then among these six faces one face must occur.
Therefore, Total number of possible outcomes = 6
Now the favourable outcome is to get an odd prime number, so between 1 to 6 the odd primes are 3 and 5, i.e, only two.
So the number of favourable outcomes =2
Therefore, we can say that,
$$\text{Probability} \left( P\right) =\dfrac{\text{Number of favourable outcomes} }{\text{Total number of possible outcomes} }$$
$$=\dfrac{2}{6}$$
$$=\dfrac{1}{3}$$
So we can say that the probability of getting an odd prime number is $$\dfrac{1}{3}$$.

Note: To solve this type of question you need to know that in mathematics, prime numbers are whole numbers which are greater than 1, that have only two factors, 1 and the number itself and they are divisible only by the number 1 or itself.
For example: 2, 3, 5, 7 and 11 are the first few prime numbers.
Also you need to have the basic idea about odd numbers, so odd numbers are those numbers which are not divisible by 2 or we can say that when divided by 2, leave a remainder 1.
For example: 1, 3, 5, 7, …...

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Solution

The correct option is BTrueThe possible outcomes when a die is rolled are 1, 2, 3, 4, 5, 6.Among the outcomes, the prime numbers are 2, 3, 5.So, the number of favourable outcomes = 3 and the number of possible outcomes = 6.∴ The probability of getting a prime number is = 36 = 12 (adsbygoogle = window.adsbygoogle || []).push({});

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