Question

Two dice, one blue and one grey, are thrown at the same time. 
(i) Write down all the possible outcomes and complete the following table:

(ii) A student argues that 'there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability \(\frac{1}{11}\)

Answer 1

(i) It can be observed that,
To get the sum as 2, possible outcomes = (1, 1) 
To get the sum as 3, possible outcomes = (2, 1) and (1, 2)
To get the sum as 4, possible outcomes = (3, 1), (1, 3), (2, 2) 
To get the sum as 5, possible outcomes = (4, 1), (1, 4), (2, 3), (3, 2) 
To get the sum as 6, possible outcomes = (5, 1), (1, 5), (2, 4), (4, 2), (3, 3)
To get the sum as 7, possible outcomes = (6, 1), (1, 6), (2, 5), (5, 2), (3, 4), (4, 3) 
To get the sum as 8, possible outcomes = (6, 2), (2, 6), (3, 5), (5, 3), (4, 4)
To get the sum as 9, possible outcomes = (3, 6), (6, 3), (4, 5), (5, 4) 
To get the sum as 10, possible outcomes = (4, 6), (6, 4), (5, 5) 
To get the sum as 11, possible outcomes = (5, 6), (6, 5) 
To get the sum as 12, possible outcomes = (6, 6)

(ii) Probability of each of these sums will not be \(\frac{1}{11}\) as these sums are not equally likely.