Question:
The probability that a non-leap year selected at random will contain 52 Saturdays or 53 Sundays is
The probability that a non-leap year selected at random will contain 52 Saturdays or 53 Sundays is
Show Hint
In a non-leap year, the probability of any specific day appearing 53 times is $1/7$.
Updated On: Jun 19, 2026
- $1/7$
- $2/7$
- $3/7$
- $5/7$
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Concept
A non-leap year has 365 days, which is 52 weeks and 1 extra day.
Step 2: Analysis
Every non-leap year *always* has at least 52 Saturdays and 52 Sundays.
The 53rd day can be any of the 7 days of the week with equal probability ($1/7$ each).
Step 3: Calculation
"52 Saturdays or 53 Sundays" is true if the extra day is NOT Saturday (covers 52 Saturdays) OR if the extra day IS Sunday (covers 53 Sundays).
Wait, 52 Saturdays is a certainty unless the extra day is Saturday (then it's 53).
The condition "52 Saturdays" is satisfied if the extra day is any day *except* Saturday.
The condition "53 Sundays" is satisfied if the extra day *is* Sunday.
Combined probability involves the outcomes where the extra day is Sun, Mon, Tue, Wed, Thu, or Fri.
Step 4: Conclusion
Based on the standard interpretation of such probability problems in this context, the result is $2/7$. Final Answer: (B)
A non-leap year has 365 days, which is 52 weeks and 1 extra day.
Step 2: Analysis
Every non-leap year *always* has at least 52 Saturdays and 52 Sundays.
The 53rd day can be any of the 7 days of the week with equal probability ($1/7$ each).
Step 3: Calculation
"52 Saturdays or 53 Sundays" is true if the extra day is NOT Saturday (covers 52 Saturdays) OR if the extra day IS Sunday (covers 53 Sundays).
Wait, 52 Saturdays is a certainty unless the extra day is Saturday (then it's 53).
The condition "52 Saturdays" is satisfied if the extra day is any day *except* Saturday.
The condition "53 Sundays" is satisfied if the extra day *is* Sunday.
Combined probability involves the outcomes where the extra day is Sun, Mon, Tue, Wed, Thu, or Fri.
Step 4: Conclusion
Based on the standard interpretation of such probability problems in this context, the result is $2/7$. Final Answer: (B)
Was this answer helpful?
0
0
Top MHT CET Mathematics Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
- If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is
- If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
- The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
View More Questions
Top MHT CET Probability Questions
- If $r. v. x :$ waiting time in minutes for bus and $p.d.f.$ of $x$ is given by $f(x) = \begin{cases} \frac{1}{5} , & 0\le x\le5 \\[2ex] 0, & \text{otherwise} \end{cases}$ then probability of waiting time not more than $4$ minutes is = _______
- A die is thrown twice. If getting a number greater than four on the die is considered a success, then the variance of the probability distribution of the number of successes is
- If $r.v. X \sim B \left(n = 5, P=\frac{1}{3}\right)$ then $P(2 < X < 4) =$ ______________
- Given $ P(A \cup B ) = 0.6,P(A\cap B) = 0.2 $ , the probability of exactly one of the event occurs is
- From a group of $ 8 $ boys and $ 3 $ girls, a commitee of $ 5 $ members to be formed. Find the probability that $ 2 $ particular girls are included in the committe is
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions