Probability Problems with Dice Eighth Grade

Probability is the chance that something will happen - how likely it is that some event will happen.If a trial will produce N commonly exclusive and equally probable outcomes out of which n outcomes are positive to the amount of event A, then the probability of A is mentioned by P(A) and is defined as the ratio n/ N. Thus the probability of A is given by

                                           Event (P)   = Number of Successful outcomes
                                                                   Number of total outcomes

probability problem with dice for 8th grade:

Problem:

A fair die is thrown. Find the probabilities that the face on the die Is 

 (1) Maximum (2) Prime (3) Multiple of 3 (4) Multiple of 7

Solution:
            In the above probability problem there are 6 possible outcomes when a die is tossed. We assumed that all the 6 faces are equally likely. The classical definition of probability is to be applied here
            

The sample space is ,S={1,2,3,4,5,6}  => n(S)=6

(1) Let A be the event that the face is maximum
            Thus,
                       A=(6),        n(A)=1
            Therefore, P(A) = n(A) / n(S)

                                  = 1/6

(2) Let B be the event that the face is prime

            Thus,
                       B=(2,3,5)        n(B)=3   
            Therefore, P(B) = n(B) / n(S)

                                  = 3/6

                                  => 1/2

(3) Let C be the event that the face is multiple of 3
            Thus,          C=(3,6)    n(C)=2
          Therefore, P(C) = n(C) / n(S)

                                = 2/6

                                =>1/3

(4) Let D be the event that the face is multiple of 7
            Thus,          D  =0,           n(D)=0
           Therefore,P(D)  = n(D)/n(S)

                                  =0/6

                                  =0   (not possible)

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Dice problem for 8th grade:

Example:

Solve the problem for probability that when 2 standard 6-sided dice are rolled, the sum of the numbers on the top faces is 4.

Solution:

In the above problem, A dice contains 6 faces, so the possible out comes from the  both dices are      

                            = 6 * 6 
                            = 36 total number of possible outcomes 
Here the given condition is “Some of the numbers on the top of the face is 4”.
So the possible out comes are 
                   Dice 1             Dice 2
                      1         +         3           = 4
                      2         +         2           = 4
                      3         +         1           = 4
the total number of successful outcomes are 3

Final solution 
                          P (sum of 4)     = 3 / 36

                                                 = 1 / 12.