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# Melissa enters a charity raffle in which bags of candy are being given

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Math Expert
Joined: 02 Sep 2009
Posts: 61510
Melissa enters a charity raffle in which bags of candy are being given  [#permalink]

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25 Nov 2019, 23:29
00:00

Difficulty:

65% (hard)

Question Stats:

25% (03:06) correct 75% (03:35) wrong based on 12 sessions

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Melissa enters a charity raffle in which bags of candy are being given away as prizes. She will be randomly assigned a number from the set of positive integers from 1 to 500 and receive a bag filled with that many pieces of candy. She decides that if the number of pieces of candy she receives is such that she can distribute the candy equally among her three children OR such that she can distribute the candy equally among her children, herself, and her husband, then she will keep it. In all other cases, she will give the candy to her neighbor if only if it can be distributed equally among the seven members of her neighbor’s family. What is the probability that Melissa gives the bag of candy to her neighbor?

A. 0.068
B. 0.076
C. 0.096
D. 0.114
E. 0.142

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Re: Melissa enters a charity raffle in which bags of candy are being given  [#permalink]

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26 Nov 2019, 03:00
We have to figure out the number of integers, which are divisible by 7, but not by 3 or 5, from 1 to 500.

N= $$[\frac{500}{7}]-[\frac{500}{3*7}]-[\frac{500}{3*5}]+[\frac{500}{3*5*7}]$$=38

Probability= 38/500= 0.076

Bunuel wrote:
Melissa enters a charity raffle in which bags of candy are being given away as prizes. She will be randomly assigned a number from the set of positive integers from 1 to 500 and receive a bag filled with that many pieces of candy. She decides that if the number of pieces of candy she receives is such that she can distribute the candy equally among her three children OR such that she can distribute the candy equally among her children, herself, and her husband, then she will keep it. In all other cases, she will give the candy to her neighbor if only if it can be distributed equally among the seven members of her neighbor’s family. What is the probability that Melissa gives the bag of candy to her neighbor?

A. 0.068
B. 0.076
C. 0.096
D. 0.114
E. 0.142

Are You Up For the Challenge: 700 Level Questions
Re: Melissa enters a charity raffle in which bags of candy are being given   [#permalink] 26 Nov 2019, 03:00
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