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A pair of fair dice is rolled.

(a) What is the probability that both dice show the same number?

(b) What is the probability that both dice show different numbers?

(c) What is the probability that the second die lands on a lower value than does the first?

 Mar 4, 2020
 #1
avatar+22043 
+2

 A pair of fair dice is rolled.

 

36 possible rolls       Six would  be same numbers     6/36 = 1/6

    All the other rolls would be DIFFERENT numbers      30/36   =  5/6

 

Subtract the = rolls...that leaves 30 rolls      1/2 of these would be second die lower      15/36  = 5/12

 Mar 4, 2020
 #2
avatar+108 
+1

A) Let's say the number on the first die is X, the second one has 1/6 of getting X

B) Let's say the first number is Y, the second has 5/6 chance of not getting Y

C) Casework

   1) 1st number is 6 second is 1, 2, 3, 4, 5 chance 1/6 times 5/6 = 5/36

   2) 1st number is 5 second is 1, 2, 3, 4 chance 1/6 times 4/6 = 4/36

   3) 1st number is 4 second is 1, 2, 3 chance 1/6 times 3/6 = 3/36

   4) 1st number is 3 second is 1, 2 chance 1/6 times 2/6 = 2/36

   5) 1st number is 2 second is 1 chance 1/6 times 1/6 = 1/36

Add them up = 15/36 = 5/12

 Mar 4, 2020
 #3
avatar+109499 
+1

(a)  P(showing  the  same  number)   =   6  /36   =   1 / 6

 

(b)  P (showing different  numbers)  =  

 

1 - P (that they show  the same numbers)  =

 

1 -  1/6   =

 

5/6

 

 

(c)  Probability  (second die  shows lesser  number than the first) =  15/36   =  5 / 12

 

 

 

 

cool cool cool

 Mar 4, 2020

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