Probabilistically Speaking, Romeo Needs To Try Harder

Discrete Mathematics Level 4

Romeo is trying to catch a glimpse of his one true love, Juliet. Juliet has been held captive by her father, and her only freedom is to stand at the balcony. She stands at the balcony at the start of the hour, twice each day, at some time from 7am to 9pm (inclusive).

Romeo can't be seen lingering outside, as the guards have orders by Juliet's father to kill him on sight. Yet, living would be meaningless if he can't see Juliet. What is the minimum number of times Romeo must pass by the balcony at the start of the hour, to have at least a 70% chance of seeing Juliet twice a day?

Details and assumptions

There are 15 possible times during the day that Juliet will be standing at the balcony.


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