Two fair dice are rolled simultaneously.Find the probability of the following events.
A: getting the same number on the both dice .
B: the product of numbers on the two dice is divisible by 2
C: the sum of numbers is grater than 5
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 product of numbers on two dice is divisible by 2.
C : the sum of numbers on two dice is greater than 5
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 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(B) = 36 - 9 = 27
Probability the product of numbers on two dice is divisible by 2. = 27/36
= 3/4
C the sum of numbers on two dice is greater than 5
= Total - sum 5 or Less
Sum 5 or less = { ( 1, 1) , ( 1, 2) , ( 1, 3) , ( 1, 4) , ( 2 ,1 ) , ( 2 ,2 ) ,( 2 , 3) , ( 3 , 1) , ( 3 ,2 ) , (4 ,1 ) }
n(C) = 36 - 10 = 26
Probability the sum of numbers on two dice is greater than 5 = 26/36
= 13/18
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