Question

Two dice are tossed. Find the probability

(a) Sum of the digits on upper face is a prime number.

(b) Digits on the upper face of the first die is less than the digit on

the second die.​

Answer 1

Answer:

a) probability = 16/30

b) probability = 9/30

Answer 2

Given,

Total outcomes when two dice are thrown = 36

To find,

We have to find the probability that

(a) Sum of the digits on the upper face is a prime number.

(b) Digits on the upper face of the first die are less than the digit on the second die.​

Solution,

The required probabilities are 15/36 and 15/36 respectively.

We can simply find the required probabilities by using the concept of probability.

(a) Number of cases when the sum on the upper face is a prime number is =  (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4,3),(5, 2), (5, 6), (6, 1), (6, 5)

P( of getting the sum of the digits on the upper face a prime number ) = 15/36

(b) Number of cases when Digits on the upper face of the first die is less than the digit on the second die = (1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)

P( of getting a number of cases when Digits on the upper face of the first die is less than the digit on the second die) = 15/36

Hence, the required probabilities are 15/36 and 15/36 respectively.