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23 Nov 2006, 04:49
Kudos
Bookmarks
Hi,
Suppose 5 marbles are placed in 5 boxes at random. Find the probability p that exactly 1 of the boxes is empty.
Could somebody solve this question with clear explantion especially in how many ways marbles are selected to place 5 marbles in 5 boxes. I thought it would be 5! ways, but it didn't work out.
Suppose 5 marbles are placed in 5 boxes at random. Find the probability p that exactly 1 of the boxes is empty.
Could somebody solve this question with clear explantion especially in how many ways marbles are selected to place 5 marbles in 5 boxes. I thought it would be 5! ways, but it didn't work out.
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23 Nov 2006, 07:24
Kudos
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Total Outcomes = 2^5 =32 -1 ( all boxes empty)
ex
consider the 5 boxes lined up, 1= marble (s) in the box, 0= no marble in the box
00000 ( not possible, since all boxes are empty)
00001 ( all 5 marbles on the last box)
00010
00100
etc..
The probability of only one become empty is 5C1=5
so P =5/31
Sorry if it's too complicated on the binary way
ex
consider the 5 boxes lined up, 1= marble (s) in the box, 0= no marble in the box
00000 ( not possible, since all boxes are empty)
00001 ( all 5 marbles on the last box)
00010
00100
etc..
The probability of only one become empty is 5C1=5
so P =5/31
Sorry if it's too complicated on the binary way
