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Home / Week 9 Exercises / Dancing Bees

Dancing Bees

The questions below are due on Tuesday April 16, 2019; 11:00:00 PM.
 
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Music For This Problem

You are a Japanese Honey Bee in a hive. Your fellow bees leave once a day and come back in the evening to report what they found during that day's flight. Because bees don't talk they communicate through dancing in order to convey what they found. The dances that bees do are comprised of combinations of the following four dance moves:

  • Shake
  • Dance in Circles
  • MoonWalk
  • Flapping Wings

A dance routine is comprised of two or more different moves performed simultaneuosly. There are four possible events that a bee could report and they are conveyed through the following dance move combinations:

  • Food Source Found: (Shake, Circles, Moonwalk)
  • Other Bees Found: (Shake, Flap, Moonwalk)
  • Japanese Giant Hornets are attacking: (Shake, Flap (and no Moonwalk))
  • Nothing to Report: (Moonwalk, Circles (and no Shake))

You may assume that these are the only four combinations of dance moves that a bee can use.

On a normal weekday for bees (Monday through Friday, inclusive),there is a probability distribution of a bee discovering the following events and returning to the hive to tell about them: DDist({'food':0.4, 'other bees': 0.1, 'Japanese Giant Hornets ATTACKING!': 0.2, 'Nothing': 0.3})

On a weekend day for bees (Saturday and Sunday), a bee has the following probability of reporting events:: DDist({'food':0.2, 'other bees': 0.3, 'Japanese Giant Hornets ATTACKING!': 0.0, 'Nothing': 0.5})

Answer the following questions; all answers should be accurate to within \(10^{-3}\). The solution boxes will accept python numerical expressions so feel free to enter your computations into them that way.

  1. On a random day, what is the probability that a specific bee returns having found food?
  2. You see a bee shaking in circles while doing the moonwalk. Based on only this information, what is the probability that it is a Tuesday?
  3. What is the probability that a specific bee's dance will involve shaking on any given day ?
  4. Because of the strobe lights and cigarette smoke, you can't see all of a bee's dance moves...but you know that it is at least shaking. What is the probability that the bee is trying to say that Japanese Giant Hornets are attacking the nest?
  5. A bee is only shaking and flapping. Based only on this information, what is the probability that it is Monday?
While European honey bees are essentially defenseless against an attack by Japanese Giant Hornets, japanese honey bees have evolved an interesting defense mechanism: see this 7-minut video from National Geographic for more information.