NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.1
Question 19

Question.  19

The probability that a non-leap year selected at random will contain 53 Sundays is

(A)

\(\dfrac{1}{7}\)

(B)

\(\dfrac{2}{7}\)

(C)

\(\dfrac{3}{7}\)

(D)

\(\dfrac{5}{7}\)

Detailed Answer with Explanation:

Step 1: A non-leap year has 365 days.

Step 2: Divide 365 days by 7 (since 1 week = 7 days).

\(365 = 52 \times 7 + 1\)

This means: 52 full weeks and 1 extra day.

Step 3: In 52 full weeks, there are exactly 52 Sundays (one in each week).

Step 4: Whether we get a 53rd Sunday depends on what that extra day is.

Step 5: The extra day can be any one of the 7 days: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, or Saturday.

Step 6: Out of these 7 possibilities, only 1 case (when the extra day is Sunday) gives us 53 Sundays.

Step 7: Therefore, the probability is:

\(\dfrac{\text{Favourable outcomes}}{\text{Total outcomes}} = \dfrac{1}{7}\)

Final Answer: Option (A) \(\dfrac{1}{7}\)

NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 13: Statistics and Probability – Exercise 13.1 | Detailed Answers