Compute the probability (round to three decimal places)

Question

1.) You want to know the probability that you will roll doubles or a sum of eight with two dice.

 

2.) If you toss four coins, what is the probability that you will get exactly 2 or 3 heads? 

Answer 1

 

1)     there are 36 possible outcomes when rolling the dice: 6 for first dice, and 6 for the second dice, and 6x6=36

 

        doubles or sum of 8

      {1,1} + {2,2} + {3,3} + {4,4} + {5,5} + {6,6} + {2,6} + {3,5} +{ 5,3} + {6,2} 

 

       10/36 = 5/18

 

2)     There are 2^4 = 16 possibilities.

 

          hhhh    hthh    thhh     tthh

          hhht     htht    thht     ttht

          hhth     htth     thth    ttth

          hhtt      httt     thtt     tttt

 

   10/16 = 5/8