Homework Help: MATH-SO LOST :(

Posted by Jen on Tuesday, July 26, 2011 at 8:38pm.

A mini license plate for a toy car must consist of a number followed by two letters. Each letter must be a C, A or R. Each number must be a 3 or 7. Repetition of letters is permitted.

Use the counting principle to determine the number of points in the sample space.
Construct a tree diagram to represent this situation.List the sample space.
Determine the exact probability of creating a mini license plate with a C. Give solution exactly in reduced fraction form.

MATH-SO LOST :( - Reiny, Tuesday, July 26, 2011 at 8:47pm
2 choices for the number, followed by 3x3 choices for the letters
number of plates = 2x3x3 = 18

the second part is somewhat ambigious.
Can both spots be C ? I will assume that

1. one C = 2x1x2 + 2x2x1 = 8
2 two C;s = 2x1x1 = 2

number of cases = 10

prob of a C = 10/18 = 5/9
MATH-SO LOST :( - Jen, Tuesday, July 26, 2011 at 8:50pm
SO CONFUSED STILL....
MATH-SO LOST :( - Reiny, Tuesday, July 26, 2011 at 8:58pm
3CC
3CA
3CR
3AA
3AC
3AR
3RR
3RA
3RC , that's 9 now do the ones starting with 7 for another 9
for a total of 18

now count how many of those 18 have a C in them .
Including the column starting with 7, I count 10 with a C in them

What part is still confusing?
MATH-SO LOST :( - Jen, Tuesday, July 26, 2011 at 9:17pm
okay...i get it now thank you Reiny :)

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