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20 Sep 2003, 12:39
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1. Suppose 5 marbles are placed in 5 boxes
at random. Find the probability p that exactly 1 of the boxes is
empty.
2. Five horses are in a race. Audrey picks 2 of the horses at random and bets on them. Find the probability that Audrey picked the winner.
at random. Find the probability p that exactly 1 of the boxes is
empty.
2. Five horses are in a race. Audrey picks 2 of the horses at random and bets on them. Find the probability that Audrey picked the winner.
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21 Sep 2003, 16:56
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Here's what I got and how:
1.
Total Possible Outcomes=Different ways of having 1, 2, 3 or 4 empty boxes respectively, each multiplied by the different ways of filling the full boxes= C(5,1)*4+C(5,2)*6+C(5,3)*4+C(5,4)*1=125
We want exactly 1 empty box= C(5,1)*4 =20
Answer=20/125
2.
1/5+4/5*1/4=2/5
1.
Total Possible Outcomes=Different ways of having 1, 2, 3 or 4 empty boxes respectively, each multiplied by the different ways of filling the full boxes= C(5,1)*4+C(5,2)*6+C(5,3)*4+C(5,4)*1=125
We want exactly 1 empty box= C(5,1)*4 =20
Answer=20/125
2.
1/5+4/5*1/4=2/5
22 Sep 2003, 03:52
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1.
The answere is : 5* (4^5) / 5^5
total number of ways that u can distribute 5 marbles in 4 boxes with any box hacing upto all marbles =( favourable out comes )
upon total outcomes : any marble in any pf the 5 boxes =5^5
2. the question can be posed as what is a probability of getting a red marble out of 5 differnt colored marbles if i were to select 2 randomly .
total outcomes : 5 C2
favorable outcome : 5
so the answere is : 5 / 5C2
The answere is : 5* (4^5) / 5^5
total number of ways that u can distribute 5 marbles in 4 boxes with any box hacing upto all marbles =( favourable out comes )
upon total outcomes : any marble in any pf the 5 boxes =5^5
2. the question can be posed as what is a probability of getting a red marble out of 5 differnt colored marbles if i were to select 2 randomly .
total outcomes : 5 C2
favorable outcome : 5
so the answere is : 5 / 5C2
