To solve this problem, we need to determine the probability that a randomly chosen month starts with the letter [tex]\( J \)[/tex] or the letter [tex]\( M \)[/tex].
Let's break down the steps to find this probability:
1. Identify the total number of months in a year:
There are [tex]\( 12 \)[/tex] months in a year.
2. Identify the months that start with the letter [tex]\( J \)[/tex]:
The months that start with [tex]\( J \)[/tex] are January, June, and July. Therefore, there are [tex]\( 3 \)[/tex] months that start with [tex]\( J \)[/tex].
3. Identify the months that start with the letter [tex]\( M \)[/tex]:
The months that start with [tex]\( M \)[/tex] are March and May. Therefore, there are [tex]\( 2 \)[/tex] months that start with [tex]\( M \)[/tex].
4. Determine the total number of months that start with either [tex]\( J \)[/tex] or [tex]\( M \)[/tex]:
- Months starting with [tex]\( J \)[/tex]: [tex]\( 3 \)[/tex]
- Months starting with [tex]\( M \)[/tex]: [tex]\( 2 \)[/tex]
Total months starting with [tex]\( J \)[/tex] or [tex]\( M \)[/tex] is [tex]\( 3 + 2 = 5 \)[/tex].
5. Calculate the probability:
The probability of a randomly chosen month starting with [tex]\( J \)[/tex] or [tex]\( M \)[/tex] is given by the number of favorable outcomes divided by the total number of possible outcomes. In this case, it is:
[tex]\[
\text{Probability} = \frac{\text{Number of months starting with } J \text{ or } M}{\text{Total number of months}} = \frac{5}{12}
\][/tex]
Therefore, the probability that a randomly chosen month starts with the letter [tex]\( J \)[/tex] or the letter [tex]\( M \)[/tex] is [tex]\(\boxed{\frac{5}{12}}\)[/tex].
