NCERT Class 12 · Ch 13 Miscellaneous Exercise · Q5
NCERT Class 12 Maths · Chapter 13 Probability · Miscellaneous Exercise Question 5
A leap year is selected at random. Find the chance of 53 Tuesdays.
💡 Concept Hints
- Define the events and identify which event is being conditioned on.
- Use P(E|F)=P(E∩F)/P(F), or separate the possible sources before applying total probability and Bayes.
✅ Step-by-Step Solution
Final Answer: 2/7 in the textbook model of equally likely starting weekdays.
- A leap year has 366=52·7+2 days. The starting weekday and the next weekday each occur 53 times.
- Tuesday is one of these extra days exactly when January 1 is Monday or Tuesday. With seven equally likely starting weekdays, the probability is 2/7. This states the model; it is not a claim that all calendar-year sampling schemes are uniform.
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