Q) Rahul and Ravi planned to play Business ( board game) in which they were supposed to use two dice.
1. Ravi got first chance to roll the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 8?
a) 
b) 
c) 
d) 0
2. Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 13?
a) 1 b) c) d) 0
3. Now it was Ravi’s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is less than or equal to 12 ?
a) 1 b) c) d) 0
4. Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is equal to 7 ?
a) 
b) c) 
d) 0
5. Now it was Ravi’s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is greater than 8 ?
a) 1 b) c) d) 
Ans:
The numbers on each dice are 1, 2, 3, 4, 5, 6.
Since each number on 1st dice can pair with each number of 2nd dice,
hence each number of 1st dice can make 6 outcomes.
Since, there are 6 numbers of 1st dice, hence, total possible outcomes = 6 x 6 = 36
1. Probability to get 8:
To get sum as 8, possible outcomes are: 2,6 3,5 4,4 5,3 6,2
∴ possible number of favorable outcomes = 5
Now the probability = 
=
Therefore, option b) is correct.
2. Probability to get 13:
Since maximum outcome possible is 6,6 and its sum is 12.
Hence, in no case, sum of both dice numbers can be 13.
∴ possible number of favorable outcomes = 0
Now the probability =
= 
= 0
Therefore, option d) is correct.
3. Probability to get less than or equal to 12:
Since all outcomes by throwing 2 dices together are either less than 12 or equal to 12, hence all outcomes are favorable outcomes.
∴ possible number of favorable outcomes = 36
Now the probability =
= 
= 1
Therefore, option a) is correct.
4. Probability to get 7:
To get sum as 7, possible outcomes are: 1,6 2,5 3,4 4,3 5,2 6,1
∴ possible number of favorable outcomes = 6
Now the probability =
= 
Therefore, option c) is correct.
5. Probability to get greater than 8:
To get sum as greater than 8, let’s calculate outcomes for each number above 8:
To get 9, possible outcomes are: 3, 6 4, 5 5, 4 6, 3
To get 10, possible outcomes are: 4, 6 5, 5 6, 4
To get 11, possible outcomes are: 5, 6 6, 5
To get 12, possible outcomes are: 6, 6
∴ possible number of favorable outcomes = 4 + 3 + 2 + 1 = 10
Now the probability =
= 
Therefore, option d) is correct.
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