Question

1. A total of 100 toys, numbered 1 through 100, are put into 100 boxes, also...

1. A total of 100 toys, numbered 1 through 100, are put into 100 boxes, also numbered 1 through 100. They are placed in such a way that toy i is equally likely to go into any of the boxes 1, 2, . . . , 100. Find the expected number of boxes that are empty. Give a numerical answer as a reduced fraction or a decimal expression accurate to at least 4 decimal places.

Math   Statistics-And-Probability   
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Answer #1

here n = k = 100

hence

expected number = 100 * (1 - 1/100)^100

= 100 * 0.99^100

= 36.6032

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