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santiago_wilson1991
Yahoo User
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 Posted: Mon Jun 16, 2008 9:13 pm Post subject: Please help me with probabilty? |
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| A mother makes a list of 5 gift ideas for Mother's Day and gives the list to each of her 5 children. If each child buys one gift on the list at random, what is the probability that at least 2 of the gifts are the same? |
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lolo <3
Yahoo User
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| Posted: Mon Jun 16, 2008 9:16 pm Post subject: |
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| 1 in 25 i think... |
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Mrs. Kelly
Yahoo User
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| Posted: Mon Jun 16, 2008 9:22 pm Post subject: |
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| Wow... I think the odds of EACH child buying a completely different gift on the list would be 1 out of 3125... so, the probability of at least 2 gifts being the same would be... 3124 out of 3125. Right?(5x5x5x5x5=3125) |
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bad panda
Yahoo User
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| Posted: Mon Jun 16, 2008 9:51 pm Post subject: |
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| The person above me is wrong because the order dose not matterFor example 12345 12354 12543 are all consider the sameIf a remeber correctly there are 120 ways you can get were no one buys the same gift5*4*3*2*1And there are 5^5 total possible combinationsThus120/3125 = Probablity that no one buys the same giftThus chance are 96.16% that at least 2 gifts are the same. |
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Skeptic
Yahoo User
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| Posted: Mon Jun 16, 2008 10:06 pm Post subject: |
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| This is the same as: 1 - P(All gifts are different)So to get this complementary probability you:Ask the first child to pick any of the five gifts: 1.0Ask the second child. It will be different 4 out of 5 times: .8Third child picks a unique gift 3 out of 5 time: .6Fourth child picks a unique gift 2 out of five times: .4Last child picks a unique gift 1 out of five times: .2This is the same as: 5/5 * 4/5 * 3/5 * 2/5 * 1/5 = 120 / 3125, orP(All gifts are different) = 1.0 * .8 * .6 * .4 * .2 = 0.0384So the probability that at least one gift is duplicated is:1 - P(All gifts are different)1 - .0384 .9616 or if you prefer fractions 3005 / 3125 = 601/621That assumes that the gift selection is independent and equally likely. The children do not talk to each other and they don't try to avoid picking the same gifts or try to pick the same gifts. This assumes the likelihood of picking each gift is the same.By the way, you should express probabilities as decimal numbers, not percentages. |
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