The probability’s higher than you think
David and Neil each have a bag of 5 balls, one of each colour: black, blue, orange, pink, and green.
David takes out a ball from his bag and puts it in Neil's, and Neil takes a ball out of his bag afterwards and puts it in David's. What is the probability that the bags will be exactly the same as before?
Note: Assume that if the colour of two balls are the same, then the balls are exactly the same.
Enter you answer as a percentage to 3 decimal places.
The answer is 33.333.
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1 solution
David putting any ball in Neil’s bag does not matter. It is Neil that decides whether the balls are same afterwards. After David puts any ball in Niel’s bag, Neil has an extra ball and two copies of the same balls. For the bags to remain the same, Neil must put either one of the same coloured ball that David gave to Neil. Since there are two copies of that ball and six balls, the probability is 6 2 , which is 33.333%