Two dice (each bearing number 1 to 6)are rolled together. Find the probability that the sum of the numbers on the upper most faces of two dice is (i) 4 or 5 . (ii) 7 , 8 or 9 . (iii) between 5 and 8. (iv) more than 10.
(Class 10 Maths Sample Question Paper)
Answers
(i) To get the sum of numbers 4 or 5 favourable outcomes are: (1, 3) ,(3, 1) , (2,2), (1, 4) , (4, 1), (2, 3) and (3,2).
Number of favourable outcomes = 7
Probability (P) =number of favourable outcomes / total number of possible outcomes
P (getting a sum 4 or 5) = 7/36
(ii) To get the sum of numbers 7,8,9 favourable outcomes are: (1, 6) ,(6, 1) , (2,5), (5, 2) , (3, 4), (4, 3) , (2,6) , (6, 2) ,(3,5) , (5,3), (4, 4) , (3, 6),(6,3),(4,5), (5,4)
Number of favourable outcomes = 15
Probability (P) =number of favourable outcomes / total number of possible outcomes
P (getting a sum 7,8 or 9) = 15/36
(iii) To get the sum of numbers between 5 & 8 i.e getting sum of 6 or 7 , favourable outcomes are: (1, 5) ,(5, 1) , (2,4), (4, 2) , (3, 3), (1, 6) , (6,1) , (2, 5) ,(5,2) , (3,4), (4, 3).
Number of favourable outcomes = 11
Probability (P) =number of favourable outcomes / total number of possible outcomes
P (getting a sum between 5 & 8) = 11/36.
(iv) To get the sum of numbers more than 10 i.e getting sum of 11 or 12 , favourable outcomes are: (5, 6) ,(6, 5) , (6,6)
Number of favourable outcomes = 3
Probability (P) =number of favourable outcomes / total number of possible outcomes
P (getting a sum more than 10) = 3 /36 = 1/12
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Answer:
Total number of possible outcomes on rolling two dice together = 36
(i) To get the sum of numbers 4 or 5 favourable outcomes are: (1, 3) ,(3, 1) , (2,2), (1, 4) , (4, 1), (2, 3) and (3,2).
Number of favourable outcomes = 7
Probability (P) =number of favourable outcomes / total number of possible outcomes
P (getting a sum 4 or 5) = 7/36
(ii) To get the sum of numbers 7,8,9 favourable outcomes are: (1, 6) ,(6, 1) , (2,5), (5, 2) , (3, 4), (4, 3) , (2,6) , (6, 2) ,(3,5) , (5,3), (4, 4) , (3, 6),(6,3),(4,5), (5,4)
Number of favourable outcomes = 15
Probability (P) =number of favourable outcomes / total number of possible outcomes
P (getting a sum 7,8 or 9) = 15/36
(iii) To get the sum of numbers between 5 & 8 i.e getting sum of 6 or 7 , favourable outcomes are: (1, 5) ,(5, 1) , (2,4), (4, 2) , (3, 3), (1, 6) , (6,1) , (2, 5) ,(5,2) , (3,4), (4, 3).
Number of favourable outcomes = 11
Probability (P) =number of favourable outcomes / total number of possible outcomes
P (getting a sum between 5 & 8) = 11/36.
(iv) To get the sum of numbers more than 10 i.e getting sum of 11 or 12 , favourable outcomes are: (5, 6) ,(6, 5) , (6,6)
Number of favourable outcomes = 3
Probability (P) =number of favourable outcomes / total number of possible outcomes
P (getting a sum more than 10) = 3 /36 = 1/12
HOPE THIS WILL HELP YOU..
Step-by-step explanation: