Two fair dice are rolled simultaneously. Find the probability of the following events :
(1) A: getting the same number on both dice.
(2) B : the sum of the integers on two dice is more than 4 but less than 8.
(3) C: the product of numbers on two dice is divisible by 2.
(4) D : the sum of numbers on two dice is greater than 12.
Answers
Given : Two fair dice are rolled simultaneously.
To Find : the probability of the following events :
(1) A: getting the same number on both dice.
(2) B : the sum of the integers on two dice is more than 4 but less than 8.
(3) C: the product of numbers on two dice is divisible by 2.
(4) D : the sum of numbers on two dice is greater than 12.
Solution:
Each dice has numbers form 1 to 6
Two fair dice are rolled simultaneously
=> Total number of events = 6 x 6 = 36
=> n(S) = 36
A: getting the same number on both dice.
=> A = { ( 1, 1) , ( 2, 2) , ( 3, 3) , ( 4 , 4) , ( 5, 5) , ( 6 , 6) }
=> n(A) = 6
probability of getting the same number on both dice. = 6/36 = 1/6
B : the sum of the integers on two dice is more than 4 but less than 8.
Sum = 5 , 6 , 7
B = { ( 1 , 4) , ( 1, 5) , ( 1 , 6) , ( 2, 3) , ( 2 ,4 ) , ( 2, 5) , ( 3 , 2) , (3 , 3) , ( 3 , 4) , ( 4 , 1) ,( 4, 2) , ( 4 , 3) , ( 5 , 1) , ( 5 , 2) , ( 6 , 1 ) }
n(B) = 15
probability of the sum of the integers on two dice is more than 4 but less than 8. = 15/36 = 5/12
C the product of numbers on two dice is divisible by 2.
if any of the two or both numbers are even = total number - both numbers odd
Both numbers odd = { ( 1, 1) , ( 1, 3) , ( 1, 5) , ( 3, 1)(3,3) , ( 3, 5) , ( 5 , 1) , (5 , 3) , ( 5, 5) )
n(C) = 36 - 9 = 27
Probability the product of numbers on two dice is divisible by 2. = 27/36
= 3/4
the sum of numbers on two dice is greater than 12.
Maximum possible sum = 6 + 6 = 12
sum of numbers on two dice is greater than 12. not possible
Hence Probability = 0
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Answer:
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