Consider the following statements :
1. The probablity that there are 53 Sundays in a leap year is twice the probability that there are 53 Sundays in a non-leap year.
2. The probability that there are 5 Mondays in the month of March is thrice the probability that there are 5 Mondays in the month of April.
Which of the statements given above is/are correct ?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Explanation

To solve the problem, we will analyze both statements one by one.

### Step 1: Analyze Statement 1
**Statement 1:** The probability that there are 53 Sundays in a leap year is twice the probability that there are 53 Sundays in a non-leap year.

**Leap Year Analysis:**
- A leap year has 366 days, which means it consists of 52 weeks and 2 extra days.
- The extra days can be any of the following pairs:
1. Sunday and Monday
2. Monday and Tuesday
3. Tuesday and Wednesday
4. Wednesday and Thursday
5. Thursday and Friday
6. Friday and Saturday
7. Saturday and Sunday

- To have 53 Sundays, one of the extra days must be a Sunday. The favorable pairs for this condition are:
- Sunday and Monday
- Saturday and Sunday

- Therefore, there are 2 favorable outcomes (Sunday and Monday, Saturday and Sunday) out of 7 possible pairs.

**Probability of 53 Sundays in a Leap Year:**
\[ P(\text{53 Sundays in Leap Year}) = \frac{2}{7} \]

**Non-Leap Year Analysis:**
- A non-leap year has 365 days, which means it consists of 52 weeks and 1 extra day.
- The extra day can be any of the following:
1. Sunday
2. Monday
3. Tuesday
4. Wednesday
5. Thursday
6. Friday
7. Saturday

- To have 53 Sundays, the extra day must be a Sunday. Thus, there is only 1 favorable outcome.

**Probability of 53 Sundays in a Non-Leap Year:**
\[ P(\text{53 Sundays in Non-Leap Year}) = \frac{1}{7} \]

**Comparison:**
- Now, we check if the probability of 53 Sundays in a leap year is twice that in a non-leap year:
\[ 2 \times P(\text{53 Sundays in Non-Leap Year}) = 2 \times \frac{1}{7} = \frac{2}{7} \]

Since \(P(\text{53 Sundays in Leap Year}) = \frac{2}{7}\), Statement 1 is **correct**.

### Step 2: Analyze Statement 2
**Statement 2:** The probability that there are 5 Mondays in the month of March is thrice the probability that there are 5 Mondays in the month of April.

**March Analysis:**
- March has 31 days, which means it consists of 4 weeks and 3 extra days.
- The extra days can be any of the following combinations:
1. Sunday, Monday, Tuesday
2. Monday, Tuesday, Wednesday
3. Tuesday, Wednesday, Thursday
4. Wednesday, Thursday, Friday
5. Thursday, Friday, Saturday
6. Friday, Saturday, Sunday
7. Saturday, Sunday, Monday

- To have 5 Mondays, we need at least one of the extra days to be a Monday. The favorable cases are:
- Sunday, Monday, Tuesday
- Monday, Tuesday, Wednesday
- Tuesday, Wednesday, Thursday
- Wednesday, Thursday, Friday
- Thursday, Friday, Saturday
- Friday, Saturday, Sunday
- Saturday, Sunday, Monday

- The favorable outcomes for having 5 Mondays are:
- Sunday, Monday, Tuesday (1)
- Monday, Tuesday, Wednesday (1)
- Saturday, Sunday, Monday (1)

Thus, there are 3 favorable outcomes.

**Probability of 5 Mondays in March:**
\[ P(\text{5 Mondays in March}) = \frac{3}{7} \]

**April Analysis:**
- April has 30 days, which means it consists of 4 weeks and 2 extra days.
- The extra days can be any of the following combinations:
1. Sunday, Monday
2. Monday, Tuesday
3. Tuesday, Wednesday
4. Wednesday, Thursday
5. Thursday, Friday
6. Friday, Saturday
7. Saturday, Sunday

- To have 5 Mondays, the extra days must include a Monday. The only favorable case is:
- Monday, Tuesday (1)

Thus, there is 1 favorable outcome.

**Probability of 5 Mondays in April:**
\[ P(\text{5 Mondays in April}) = \frac{1}{7} \]

**Comparison:**
- Now we check if the probability of 5 Mondays in March is thrice that in April:
\[ 3 \times P(\text{5 Mondays in April}) = 3 \times \frac{1}{7} = \frac{3}{7} \]

Since \(P(\text{5 Mondays in March}) = \frac{3}{7}\), Statement 2 is **correct**.

### Conclusion
Both statements are correct. Therefore, the answer is that both statements are correct.

### Final Answer
Both statements 1 and 2 are correct.