MHB Find the probability that all 7 witnesses would pick the same person.

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In a homicide case with 7 witnesses identifying a suspect from a lineup of 5 men, the probability that all witnesses would randomly pick the same person is calculated. Each of the last 6 witnesses has a 1/5 chance of matching the first witness's choice. This results in a probability of (1/5) raised to the power of 6, equating to 1 in 15625. This means that out of a million attempts, this scenario would occur approximately 64 times. The calculation highlights the rarity of such unanimous identification by random guessing.
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In a homicide case, 7 different witnesses picked the same man from a lineup. The line up contained 5 men. If the identification were made by random guesses, find the probability that all 7 witnesses would pick the same person.
 
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Hint: the last 6 witnesses each have probability 1/5 of matching 1st witness.
 
Btw, that means exactly 64 times out of a million attempts!
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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