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 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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