Math, asked by panandi38190, 7 months ago

Two fair dice are rolled simultaneously. Find probability of events
(i) getting same number on both dice. (ii) sum of integers on two
dice is more than 4 but less than 8. (iii) product of numbers on
two dice is divisible by 2 OR product of two number is even. (iv)
sum of numbers on two dice is greater than 12.
hability of (i) getting at least 2

Answers

Answered by Anonymous

NANBA..

where the first number in the parenthesis is the outcome of the first die and the second number is the outcome of the second die. So then the probability of two rolled dice having the same number becomes 6/36, which reduces to 1/6. A pair of fair dice is thrown independently 3 times..

Answered by amitnrw

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 or even

(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