Question

Two fair dice are rolled simultaneously. Find the probability of the following events,
A: getting the same number on both dice
(ii) B : The sum of the integers on two dice is more than 4 but less than 8
(iii) C: The product of numbers on two dice is greater than 12​

Answer 1

Answer:

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 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 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

_________________________________

Learn from Brainly.in  {PROBABILTY}

• https://brainly.in/question/15716115
• https://brainly.in/question/18763127
• https://brainly.in/question/15820235
• https://brainly.in/question/17337821

Answer 2

Answer:

A) the probability is 1/6

B)the probability is 5/12

C) the probability is 0