math

how do you explain this questionA mini license plate for a toy car must consist of a letter followed by two numbers. Each letter must be a T, O or Y. Each number must be a 4 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 a Y. Give solution exactly in reduced fraction form.

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  1. Number of ways
    = 3 x 2 x 2 = 12

    I will list the cases that start with T
    T44
    T46
    T64
    T66
    You can do the same thing starting with O and Y

    Your tree will have 3 main branches, ending in T, O , and Y
    Each of those ends will have 4 branches coming off it, representing the 4 different number combinations.

    Prob(plate with a Y) = 4/12 = 1/3

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