HardMathematicsHigh School (9–10)GeneralStatistics and Probability › ProbabilityConceptualNumericalSAT
A leap year is chosen at random. Find the probability that it has 53 Sundays.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A leap year is chosen at random. Find the probability that it has Sundays.
Need a reminder? The key ideaShow
For balls, discs or spinners with equally likely outcomes, . To find an unknown number of balls, write the probability with the unknown and solve the equation. An event and its complement add up to .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Extra days. , so there are full weeks and extra days.
Step 2. The pairs. The two extra days are consecutive: (Sun, Mon), (Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri), (Fri, Sat), (Sat, Sun). That is equally likely pairs.
Step 3. Favourable. A rd Sunday needs a Sunday among the extra days: (Sun, Mon) and (Sat, Sun), so pairs.
Answer: .
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