Question

(i) Two dice are rolled simultaneously. Find the probability of the following even
ents.
(1) The sum of the digits on the upper surface is a prime number.
(2) The product of the digits on the upper surface is 12.
(3) The digit on the first die is greater than the digit on the second die.
11.
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Answer 1

Answer:

1) 4/6 = 2/3

2) 1/6

Step-by-step explanation:

Answer 2

Step-by-step explanation: There are total 36 combinations of dice rolls .

They are (1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3) and so on till (6,5)(6,6) .

1. From these , there are total 15 combinations such that the sum of the two digits dropped is a prime . They are (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) . So probability of getting such combinations is 15/36 or 5/12 .
2. There are total 4 combinations such that the product of the digits dropped is 12 . They are (2,6)(3,4)(4,3)(6,2) So probability of getting such combinations is 4/36 or 1/9 .
3. There are total 15 combinations such that the digit on the first side is greater than the digit on the second side . They are (2,1)(3,1)(3,2)(4,1)(4,2)(4,3)(5,1)(5,2)(5,3)(5,4)(6,1)(6,2)(6,3)(6,4)(6,5). So probability of getting such combinations is 15/36 or 5/12 .

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