Given: A dice is thrown once

Required to find:

(i) Probability of getting a prime number

(ii) Probability of getting 2 or 4

(iii) Probability of getting a multiple of 2 or 3.

(iv) Probability of getting an even number

(v) Probability of getting a number greater than five.

(vi) Probability of lying between 2 and 6

Total number on a dice is 6 i.e., 1, 2, 3, 4, 5 and 6.

(i) Prime numbers on a dice are 2, 3, and 5. So, the total number of prime numbers is 3.

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, probability of getting a prime number = \(\frac{3}{6}\) = \(\frac{1}{2}\)

(ii) For getting 2 and 4, clearly the number of favourable outcomes is 2.

We know that Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting 2 or 4 = \(\frac{2}{6}\) = \(\frac{1}{3}\)

(iii) Multiple of 2 are 3 are 2, 3, 4 and 6.

So, the number of favourable outcomes is 4

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting an multiple of 2 or 3 = \(\frac{4}{6}\) = \(\frac{2}{3}\)

(iv) An even prime number is 2 only.

So, the number of favourable outcomes is 1.

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting an even prime number = \(\frac{1}{6}\)

(v) A number greater than 5 is 6 only.

So, the number of favourable outcomes is 1.

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a number greater than 5 = \(\frac{1}{6}\)

(vi) Total number on a dice is 6.

Numbers lying between 2 and 6 are 3, 4 and 5

So, the total number of numbers lying between 2 and 6 is 3.

We know that, Probability = Number of favourable outcomes/ Total number of outcomes

Thus, the probability of getting a number lying between 2 and 6 = \(\frac{3}{6}\) = \(\frac{1}{2}\)