To determine the probability that a randomly chosen month of the year starts with the letter 'J' or 'M', we can follow these steps:
1. Identify the total number of months in a year:
There are 12 months in a year.
2. Identify the months that start with the letter 'J':
- January
- June
- July
So, there are 3 months that start with the letter 'J'.
3. Identify the months that start with the letter 'M':
- March
- May
So, there are 2 months that start with the letter 'M'.
4. Calculate the total number of months that start with 'J' or 'M':
Combining the months from both categories:
[tex]\( 3 \text{ (months starting with 'J')} + 2 \text{ (months starting with 'M')} = 5 \text{ months} \)[/tex]
5. Calculate the probability:
The probability [tex]\( P \)[/tex] of selecting a month that starts with 'J' or 'M' is the ratio of the number of favorable outcomes to the total number of possible outcomes.
[tex]\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{5}{12}
\][/tex]
Given the multiple-choice options provided, the correct answer is indeed:
[tex]\[
\frac{5}{12}
\][/tex]
Thus, the probability that a randomly chosen month starts with the letter 'J' or 'M' is [tex]\(\frac{5}{12}\)[/tex], which corresponds to approximately 0.4167.
