After a week of slicing up cakes and pizzas, here’s a PMQ with a similar theme.

Take a circle and randomly draw three distinct diameters, thereby partitioning the circle into six sectors. What is the probability that two of the sectors each has an area that is at least a quarter of the circle?

Just a note, that you may pick any random method, e.g., a random number generator for the angle of a diameter with respect to some zero point. Depending on your chosen method, you may end up with either a discrete or continuous function; it will be interesting to see how their results differ, and I shall accept both versions. You may, of course, come up with an altogether different method!

Have fun!

**IMPORTANT CHANGES TO THE PRIZE MATHS QUIZ!**

**YOU MAY NOW DISCUSS THIS PMQ PROBLEM IN THE COMMENTS BELOW AND GIVE YOUR ANSWERS AND SOLUTION METHOD.**

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**How to Enter****IF YOU ARE A STUDENT, you may still send your complete solution by email to pmq33bernoulli@giftedmaths.com.**This email address shall be removed after the competition closes to avoid spam.

**This PMQ33 competition closes on WEDNESDAY 28 AUGUST at 23:59 GMT.**

**The Prize****The prizes for this PMQ are 3 free places in our Online Maths Club for ONE YEAR.**The very first correct solution will receive a prize plus two others randomly selected from all the other correct answers. The email time stamp shall determine the order of entries received. All winners can have their name posted and a link to their own online profile at their favourite social network or their own blog.

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Enjoy the challenge!

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