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# A customer wants to buy a total of 8kg rice of two varieties- A an

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A customer wants to buy a total of 8kg rice of two varieties- A an  [#permalink]

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Updated on: 27 Apr 2018, 05:04
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Difficulty:

55% (hard)

Question Stats:

62% (01:47) correct 38% (02:20) wrong based on 114 sessions

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3 deadly mistakes you must avoid in Probability - Exercise Question #2

2- A customer wants to buy a total of 8kg rice of two varieties- A and B. If he can buy each type of rice only in integral multiples of 1 kg then what is the probability that he will buy at least 2 kg rice of each variety?

Options
a) 1/3
b) 4/9
c) 5/9
d) 5/8
e) 2/3

To solve question 3:Question 3

To read the article: 3 deadly mistakes you must avoid in Probability

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Originally posted by EgmatQuantExpert on 26 Apr 2018, 04:30.
Last edited by EgmatQuantExpert on 27 Apr 2018, 05:04, edited 2 times in total.
e-GMAT Representative
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A customer wants to buy a total of 8kg rice of two varieties- A an  [#permalink]

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Updated on: 29 Apr 2018, 01:35

Solution

Given:

• The customer wants to buy 8 kg of rice.
• The rice is of two types- A and B.
• The customer can buy each type of rice only in integral multiples of a kg.

To find:
• The probability such that the customer buys 2kg rice of each variety.

Approach and Working:

We can solve this problem from two methods:

• By calculating the probabilities of the independent cases
o 2 kg Rice A and 6 kg rice B
o 3 kg Rice A and 5 kg rice B
o 4 kg Rice A and 4 kg rice B
o 5 kg Rice A and 3 kg rice B
o 6 kg Rice A and 2 kg rice B

• By non-event method
o P (customer buys 2kg rice of each variety) = 1- P(customer buys 0 kg rice of one variety)- P(customer buys 1 kg rice of one variety)

Clearly, the 2nd method reduces a lot of calculation.

P(customer buys 0 kg rice of one variety):

• There are 2 possible ways in which he can buy 0 kg rice of one variety.
o When he buys 8 kg rice of type A.
o When he buys 8 kg rice of type A.
• Thus, P (customer buys 0 kg rice of one variety) = 2/9

P(customer buys 1 kg rice of one variety):
• There are 2 possible ways in which he can buy 1 kg rice of one variety.
o When he buys 1 kg rice of type A and 1 kg rice of type B.
o When he buys 1 kg rice of type B and 7 kg rice of type B.
• Thus, P (customer buys 0 kg rice of one variety) = 2/9

Hence, P (customer buys 2kg rice of each variety) = 1- 2/9-2/9= 5/9
Hence, the correct answer is option C.

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Originally posted by EgmatQuantExpert on 26 Apr 2018, 04:31.
Last edited by EgmatQuantExpert on 29 Apr 2018, 01:35, edited 1 time in total.
Manager
Joined: 25 Apr 2016
Posts: 59
Re: A customer wants to buy a total of 8kg rice of two varieties- A an  [#permalink]

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26 Apr 2018, 04:40
Total no. of cases lie from the range of (8,0) to (0,8) => 9 cases
and no. of favorable ones would be (2,6),(3,5),(4,4),(5,3), and (6,2)
=> probability=5/9
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Re: A customer wants to buy a total of 8kg rice of two varieties- A an  [#permalink]

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27 Apr 2018, 00:01
Integral solutions to the equation A+B = x = x+2-1 C 1

Since A , B have to be at least 2 each the equation becomes A+B=4.
Number of solutions = 5C1 = 5.

Total possible solutions = 9C1 = 9.

Hence C.
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Manager
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Posts: 97
Re: A customer wants to buy a total of 8kg rice of two varieties- A an  [#permalink]

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27 Apr 2018, 02:27
attari92 wrote:
Total no. of cases lie from the range of (8,0) to (0,8) => 9 cases
and no. of favorable ones would be (2,6),(3,5),(4,4),(5,3), and (6,2)
=> probability=5/9

hi i have a confusion...here..

how one can take (8,0) and (0,8)
it is given a person need two take 8 kg of rice of two varieties...there must be two varieties in 0,8 and 8,0 the variety is only one..
Manager
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Posts: 59
Re: A customer wants to buy a total of 8kg rice of two varieties- A an  [#permalink]

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27 Apr 2018, 03:04
viv007 wrote:
attari92 wrote:
Total no. of cases lie from the range of (8,0) to (0,8) => 9 cases
and no. of favorable ones would be (2,6),(3,5),(4,4),(5,3), and (6,2)
=> probability=5/9

hi i have a confusion...here..

how one can take (8,0) and (0,8)
it is given a person need two take 8 kg of rice of two varieties...there must be two varieties in 0,8 and 8,0 the variety is only one..

I put the two varieties in an ordered pair, just a gesticulation of representation. And, there isn't anything wrong in considering range from (8,0) to (0,8) as it symbolizes the entire sample space.
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Re: A customer wants to buy a total of 8kg rice of two varieties- A an  [#permalink]

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29 Apr 2018, 01:36
Hey everyone,

The official answer to the question has been posted.

Regards,
Ashutosh
_________________

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Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
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Senior Manager
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A customer wants to buy a total of 8kg rice of two varieties- A an  [#permalink]

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30 Apr 2018, 17:42
1
EgmatQuantExpert wrote:
Hey everyone,

The official answer to the question has been posted.

Regards,
Ashutosh

Can you rephrase the question to "he needs to buy 8 kg. There are two kinds of rice..."? Otherwise the question sounds ambiguous, since he have to buy 8 kg of both kinds, and people are confused. Thanks
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Joined: 23 Mar 2017
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GRE 1: Q800 V660
Re: A customer wants to buy a total of 8kg rice of two varieties- A an  [#permalink]

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28 May 2018, 10:01
For calculating the total number of outcomes, is counting the best method? Can't figure out any alternative approach.
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Joined: 03 Jul 2015
Posts: 11
Re: A customer wants to buy a total of 8kg rice of two varieties- A an  [#permalink]

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28 May 2018, 23:41
EgmatQuantExpert wrote:

Solution

Given:

• The customer wants to buy 8 kg of rice.
• The rice is of two types- A and B.
• The customer can buy each type of rice only in integral multiples of a kg.

To find:
• The probability such that the customer buys 2kg rice of each variety.

Approach and Working:

We can solve this problem from two methods:

• By calculating the probabilities of the independent cases
o 2 kg Rice A and 6 kg rice B
o 3 kg Rice A and 5 kg rice B
o 4 kg Rice A and 4 kg rice B
o 5 kg Rice A and 3 kg rice B
o 6 kg Rice A and 2 kg rice B

• By non-event method
o P (customer buys 2kg rice of each variety) = 1- P(customer buys 0 kg rice of one variety)- P(customer buys 1 kg rice of one variety)

Clearly, the 2nd method reduces a lot of calculation.

P(customer buys 0 kg rice of one variety):

• There are 2 possible ways in which he can buy 0 kg rice of one variety.
o When he buys 8 kg rice of type A.
o When he buys 8 kg rice of type A.
• Thus, P (customer buys 0 kg rice of one variety) = 2/9

P(customer buys 1 kg rice of one variety):
• There are 2 possible ways in which he can buy 1 kg rice of one variety.
o When he buys 1 kg rice of type A and 1 kg rice of type B.
o When he buys 1 kg rice of type B and 7 kg rice of type B.
• Thus, P (customer buys 0 kg rice of one variety) = 2/9

Hence, P (customer buys 2kg rice of each variety) = 1- 2/9-2/9= 5/9
Hence, the correct answer is option C.

Hello - i dont understand how to get the 9 denominator, mind to explain ?
Re: A customer wants to buy a total of 8kg rice of two varieties- A an &nbs [#permalink] 28 May 2018, 23:41
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# A customer wants to buy a total of 8kg rice of two varieties- A an

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