Maths Problem

1.     A six-sided dice was rolled once. Find:

a.     the probability of obtaining the even-spot sides or the odd-spot sides;

b.     the probability of obtaining the even-spot sides or the sides with spot greater than 3.

(Marsigit,2009:131)

Answer

Data  : The sample space of the results of throwing a six-sided dice once is S={1,2,3,4,5,6}. So, the total member of sample space is n(S)=6.

Find   : a. the probability of obtaining the even-spot sides or the odd-spot sides; b. the probability of obtaining the even-spot sides or the sides with spot greater than 3.

Solution:

a.     If A is an event of occurrences of sides with even-spot, then A={2,4,6}. The total member of event A is n(A)=3. If B is an event of occurrences of sides with odd-spot, the B={1,3,5}. The total member of event B is n(B)=3.

Then, we can conclude that A∩B=∅. So, A and B are mutually exclusive events.

As a results,

   

So, the probability of occurrances of side with even-spot or the sides with odd-spot is . It means this kind of event is exactly happening.

b.     If C is an event of occurrances of sides with even-spot, then C={2,4,6}. The total member of event C is n(C)=3. If D is an event of occurrances of sides with spot greater than 3, then D={4,5,6}. The total member of event D is n(D)=3.

Then, we can conclude that C∩D={4,6}. So, C and D are non-mutually exclusive events with n(C∩D)=2.

As a results,

       

      

So, the probability of occurrances of sides with even-spot or the sides with spot greater than 3 is .