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# Question of the Week- 19 (A store sells equal number of Vanilla .....)

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Question of the Week- 19 (A store sells equal number of Vanilla .....)  [#permalink]

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Updated on: 19 Oct 2018, 06:34
00:00

Difficulty:

65% (hard)

Question Stats:

62% (02:35) correct 38% (02:22) wrong based on 148 sessions

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Question of the Week #19

A store sells equal number of Vanilla and Coco flavoured candies, each in one of the coloured wrappers: Red, Green, Blue, and Violet. The ratio of total number of Red, Green, Blue, and Violet candies is 2:3:4:1, in every flavour. Now, without seeing the colour of the wrapper, Harry randomly picked up one of the candies, hoping that it will be a Green Vanilla flavoured candy. What is the probability that the selected candy will have at least one of the two features, wished by Harry?

A. $$\frac{1}{2}$$

B. $$\frac{11}{20}$$

C. $$\frac{13}{20}$$

D. $$\frac{4}{5}$$

E. $$\frac{17}{20}$$

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Originally posted by EgmatQuantExpert on 19 Oct 2018, 03:24.
Last edited by EgmatQuantExpert on 19 Oct 2018, 06:34, edited 1 time in total.
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Re: Question of the Week- 19 (A store sells equal number of Vanilla .....)  [#permalink]

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19 Oct 2018, 06:27
2
1
Ratio of color = 2:3:4:1. Total = 10x out of which 5x is vanilla and 5x is coco.
Probability of green = 3/10 ; Not green = 7/10
Probability of vanilla = 1/2 ; coco = 1/2
Probability of at least one of the two features of Green Vanilla = 1- None of the feature
= 1 - 7/10 * 1/2
= 13/20

Option C
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Re: Question of the Week- 19 (A store sells equal number of Vanilla .....)  [#permalink]

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19 Oct 2018, 09:34
You could also quickly write down a simple table to count the desired outcomes, then divide that by the total number of outcomes to obtain the probability.

We see that we have 10 coco flavoured candy + 3 green vanilla candy, which makes 13 out of a total of 20 available candy.

p = 13 / 20

Attachments

table.png [ 3.1 KiB | Viewed 964 times ]

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Re: Question of the Week- 19 (A store sells equal number of Vanilla .....)  [#permalink]

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24 Oct 2018, 01:05
1

Solution

Given:
• A store sells equal number of Vanilla and Coco flavoured candies, each in one of the coloured wrappers: {Red, Green, Blue and Violet}
• The ratio of total number of red, green, blue and violet candies is 2: 3: 4: 1, in every flavour
• Wishing a green vanilla flavoured candy, Harry randomly picked up one candy

To find:
• The probability that the selected candy will be either Green coloured or Vanilla flavoured or both.

Approach and Working:
• Let us assume the total number of candies = 20x
• Then, the number of vanilla and coco flavoured candies will be = 10x and 10x.
• And, the number of red, green, blue and violet candies, in each of the two flavours, are 2x, 3x, 4x and x respectively

• Now, from the above table, we can see that the number of candies which are either green coloured or vanilla flavoured = 2x + 3x + 4x + x + 3x = 13x
• Therefore, the probability = $$\frac{13x}{20x} = \frac{13}{20}$$

Hence, the correct answer is option C.

Note: The logic behind assuming the total number of candies as 20x is that there are a total of 20 parts ((2+ 3 + 4 +1)*2) of candies of different flavours packed in different coloured wrappers.

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Re: Question of the Week- 19 (A store sells equal number of Vanilla .....)  [#permalink]

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30 Nov 2018, 02:27
Much easier if you approach it as P(a) + P(b) - P(a&b)
50% +30% - 15% = 65%
Re: Question of the Week- 19 (A store sells equal number of Vanilla .....)   [#permalink] 30 Nov 2018, 02:27
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