Two dice are rolled together. Find the probability that the sum of the numbers on the uppermost faces of two dice is 1. 4 or 5 2. 7,8 or 9 3. Between 5 and 8 4. More than 10
Answers
Given : Two dice are rolled together
To Find : probability that the sum of the numbers on the uppermost faces of two dice is
1. 4 or 5
2. 7,8 or 9
3. Between 5 and 8
4. More than 10
Solution:
Two dice are rolled together.
Number of ways = 6 * 6 = 36
sum of the numbers on the uppermost faces of two dice is 4
4 = ( 1 ,3 ) , ( 2, 2) , ( 3, 1)
5 = ( 1 ,4 ) , ( 2 . 3) ( 3, 2) , ( 4, 1)
Total ways = 7
Probability that sum 4 or 5 = 7/36
Sum 7 , 8 or 9
7 = ( 1, 6) , ( 2, 5) , ( 3, 4) , ( 4, 3) , ( 5 , 2) , ( 6 , 1)
8 = ( 2, 6) , ( 3 , 5) , ( 4 , 4) , ( 5. 3) , ( 6 , 2)
9 = ( 3, 6) , ( 4, 5) , ( 5 , 4) ,( 6 , 3)
Total ways = 15
Probability that sum 7,8 or 9 = 15/36 = 5/12
Between 5 and 8
Mean 6 & 7
6 = ( 1, 5) , ( 2, 4) , ( 3, 3) , ( 4, 2) , ( 5 , 1)
7 = ( 1, 6) , ( 2, 5) , ( 3, 4) , ( 4, 3) , ( 5 , 2) , ( 6 , 1)
Total ways = 11
Probability that sum Between 5 and 8 = 11/36
More than 10
11 or 12
11 = ( 5 , 6) 6 , 5)
12 = { 6 , 6)
Total ways = 3
Probability that sum More than 10 = 3/36 = 1/12
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