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
A non-leap year has 52 weeks and one extra day; use the union formula for the two events.
Updated On: Nov 13, 2026
\(\frac{1}{7}\)
\(\frac{6}{7}\)
\(\frac{2}{7}\)
\(\frac{5}{7}\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
365 days = 52 weeks + 1 extra day, and each of the 7 weekdays is equally likely to be the extra day.
Step 2: Find the probabilities
\(P(52\text{ Saturdays})=P(\text{extra day is not Saturday})=\dfrac{6}{7}\).
\(P(53\text{ Sundays})=\dfrac{1}{7}\).
Step 3: Intersection
Both hold if the extra day is Sunday: \(P=\dfrac{1}{7}\).
Step 4: Union
\(P=\dfrac{6}{7}+\dfrac{1}{7}-\dfrac{1}{7}=\dfrac{6}{7}\).
Final Answer:
The probability is 6/7. \[ \boxed{\text{(B) }\dfrac{6}{7}} \]
365 days = 52 weeks + 1 extra day, and each of the 7 weekdays is equally likely to be the extra day.
Step 2: Find the probabilities
\(P(52\text{ Saturdays})=P(\text{extra day is not Saturday})=\dfrac{6}{7}\).
\(P(53\text{ Sundays})=\dfrac{1}{7}\).
Step 3: Intersection
Both hold if the extra day is Sunday: \(P=\dfrac{1}{7}\).
Step 4: Union
\(P=\dfrac{6}{7}+\dfrac{1}{7}-\dfrac{1}{7}=\dfrac{6}{7}\).
Final Answer:
The probability is 6/7. \[ \boxed{\text{(B) }\dfrac{6}{7}} \]
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