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Independent and Mutually Exclusive Events Pre-Test

1. A month of the year is chosen at random. What is the probability that the month starts with the letter [tex]J[/tex] or the letter [tex]M[/tex]?

A. [tex]\frac{5}{24}[/tex]
B. [tex]\frac{1}{6}[/tex]
C. [tex]\frac{1}{4}[/tex]
D. [tex]\frac{5}{12}[/tex]



Answer :

GinnyAnswer
To determine the probability that a randomly chosen month starts with the letter 'J' or the letter 'M', we need to follow a series of steps.

### Step-by-Step Solution:

1. List Total Number of Months:
There are 12 months in a year.

2. Identify Months Starting with 'J' and 'M':
- Months starting with 'J':
- January
- June
- July
Thus, the number of months starting with 'J' is 3.

- Months starting with 'M':
- March
- May
Thus, the number of months starting with 'M' is 2.

3. Calculate Total Number of Months Starting with 'J' or 'M':
- Since a month cannot start with both letters simultaneously, the events are mutually exclusive.
- Adding the number of months starting with 'J' (3) and the number of months starting with 'M' (2):
Total number of months starting with 'J' or 'M' = 3 + 2 = 5

4. Calculate the Probability:
- Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
- Therefore, the probability that a month starts with 'J' or 'M' is given by:
[tex]\[ \text{Probability} = \frac{\text{Number of months starting with 'J' or 'M'}}{\text{Total number of months}} = \frac{5}{12} \][/tex]

5. Match the Probability to Given Options:
- We are given four possible fractions:
[tex]\[ \frac{5}{24}, \frac{1}{6}, \frac{1}{4}, \frac{5}{12} \][/tex]
- As calculated, the probability of \(\frac{5}{12}\) is one of the options.

Hence, the correct answer corresponding to the probability that a chosen month starts with the letter 'J' or the letter 'M' is:
[tex]\[ \boxed{\frac{5}{12}} \][/tex]

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