The probability that a motorcycle has a license plate containing a double letter and an even number \(\boxed{\frac{1}{{52}}}.\)
Further explanation:
The probability can be obtained as the ratio of favorable number of outcomes to the total number of outcomes.
\(\boxed{{\text{Probability}} = \frac{{{\text{Favorable number of outcome}}}}{{{\text{Total number of outcomes}}}}}\)
Given:
A motorcycle license plate has 2 letters and 3 numbers.
Explanation:
There are 26 letters.
The double letters are as follows,
\(S = \left( {aa,bb,cc, \ldotszz} \right)\)
The total numbers of double letters are \(\boxed{26}\)
The total number of even numbers can be obtained as follows,
\(\begin{aligned}{\text{Total numbers}} &= 10 \times 10 \times 5\\&= 500\\\end{aligned}\)
The favorable number of outcomes can be obtained as follows,
\(\begin{aligned}{\text{Favourable number of outcomes}} &= 26 \times 500 \\ &= 13000\\\end{aliged}\)
The total numbers of outcomes can be obtained as follows,
\(\begin{aligned}{\text{Total number of outcomes}}&= 26 \times 26 \times 10 \times 10 \times 10 \\&= 676000\\\end{aligned}\)
The probability that a motorcycle has a license plate containing a double letter and an even number \(\boxed{\frac{1}{{52}}}.\)
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: motorcycle, license plate, 2 letters, 3 numbers, probability, motorcyclist, containing, double letter, even numbers, odd numbers.
