To determine the probability that a randomly chosen month starts with the letter [tex]\( J \)[/tex] or the letter [tex]\( M \)[/tex], we need to follow these steps:
1. Identify the total number of months in a year.
There are 12 months in a year.
2. Determine which months start with the letter [tex]\( J \)[/tex].
The months that start with the letter [tex]\( J \)[/tex] are January, June, and July. This gives us 3 months.
3. Determine which months start with the letter [tex]\( M \)[/tex].
The months that start with the letter [tex]\( M \)[/tex] are March and May. This gives us 2 months.
4. Calculate the total number of favorable months.
The favorable months are those starting with either [tex]\( J \)[/tex] or [tex]\( M \)[/tex].
- Number of months starting with [tex]\( J \)[/tex] = 3
- Number of months starting with [tex]\( M \)[/tex] = 2
- Total favorable months [tex]\( = 3 + 2 = 5 \)[/tex]
5. Calculate the probability.
The probability [tex]\( P \)[/tex] of choosing a month that starts with either [tex]\( J \)[/tex] or [tex]\( M \)[/tex] is the number of favorable outcomes divided by the total number of possible outcomes.
[tex]\[
P = \frac{\text{Number of favorable months}}{\text{Total number of months}} = \frac{5}{12}
\][/tex]
Hence, the probability that a randomly chosen month starts with the letter [tex]\( J \)[/tex] or the letter [tex]\( M \)[/tex] is [tex]\( \frac{5}{12} \)[/tex].
The correct answer is [tex]\( \boxed{\frac{5}{12}} \)[/tex].
