Question

A mini license plate for a toy car must consist of a letter followed by two numbers. Each letter must be an R, U or N. Each number must be a 2 or 6. Repetition of digits 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 an R. Give solution exactly in reduced fraction form.

Answer 1

the tree diagram would be the 2 and 6 on top and then 3 lines down from each one and then R U N right?
then 3 more lines down and then repeat R U N

Answer 2

there are
\[3\times 2\times 2=12\] elements in the sample space
sample space is
R 1 1
R 1 2
R 2 1
R 2 2
U 1 1
U 1 2
U 2 1
U 2 2
N 1 1
N 1 2
N 2 1
N 2 2

Answer 3

you have 3 letters to choose from, one is an R so the probability of creating a plate beginning with R is
\[\frac{1}{3}\]

Answer 4

also notice of course that
\[\frac{4}{12}=\frac{1}{3}\]

Answer 5

do you know how to construct the tree ?

Answer 6

yes..

Answer 7

stupid tree