A mini license plate for a toy car must consist of a twoletters followed by a on

Question

A mini license plate for a toy car must consist of a twoletters followed by a on digit odd number each letter must be a Qor Z repetition of letters is premitted. 1) use the counting principle to determine the number ofpoints in the sample space. 2) construct a tree diagram to represent this situation 3)list the sample space 4)determine the exact probability of creating a mini licenseplate with a 3 give solution in reduced fraction form. A mini license plate for a toy car must consist of a twoletters followed by a on digit odd number each letter must be a Qor Z repetition of letters is premitted. 1) use the counting principle to determine the number ofpoints in the sample space. 2) construct a tree diagram to represent this situation 3)list the sample space 4)determine the exact probability of creating a mini licenseplate with a 3 give solution in reduced fraction form.

Explanation / Answer

1.)   letter1      letter2      number             The 1st letter can be Qor Z.       The 2nd letter can also be Q orZ.       The number can be 1,3,5,7or,9. Hence, using the counting principle , there are 2*2*5=20points in the sample space. 3.)Sample space: S={QQ1,QQ3,QQ5,QQ7,QQ9,       QZ1,QZ3,QZ5,QZ7,QZ9,       ZQ1,ZQ3,ZQ5,ZQ7,ZQ9,       ZZ1,ZZ3,ZZ5,ZZ7,ZZ9} Hence, number of elements of the sample space=20. 4.) QQ3,QZ3,ZQ3,ZZ3 probability of creating a mini license plate with a3   : 4/20=1/5             

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