Probability and Statistics

Question

Five different coins are in a bag. Three are drawn. I've 2 of the different coins. What are the chances my coins match the 3 drawn? Explain.

Answer 1

The chance is zero. All coins are different.

Answer 2

Hi Mark -- 2 different pockets each have 5 different coins. Take a trio from the left pocket; pull a pair from the right pocket. Does the pair match what's available in the trio? Simplify by looking at the pair first:

AB CDE : pairs AB,AC,AD,AE ... BC,BD,BE ... CD,CE .. DE => "AB" is 1/10 or 10% chance of right-pocket pairs. ABC DE : trios ABC,ABD,ABE ... ACD,ADE,ACE ... BCD,BCE,BDE ... CDE => "ABx" is 3/10 or 30% of left trios.

Looks like chance of "AB" pair matching with "ABx" trio is 1/10(3/10) or 3/100 ==> 3% chance.

To check this, try sampling this experiment ten times and there probably would not be a single match ... Regards, sir :)