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Question of the Week- 19 (A store sells equal number of Vanilla .....) Updated on: 19 Oct 2018, 06:34
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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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

63% (02:30) correct 37% (02:28) wrong based on 679 sessions

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e-GMAT 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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C
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Question of the Week- 19 (A store sells equal number of Vanilla .....) 19 Oct 2018, 06:27
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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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Question of the Week- 19 (A store sells equal number of Vanilla .....) 19 Oct 2018, 09:34
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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

Answer C
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Question of the Week- 19 (A store sells equal number of Vanilla .....) 24 Oct 2018, 01:05
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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.

Answer: 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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Question of the Week- 19 (A store sells equal number of Vanilla .....) 30 Nov 2018, 02:27
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Much easier if you approach it as P(a) + P(b) - P(a&b)
50% +30% - 15% = 65%
Answer is C
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Question of the Week- 19 (A store sells equal number of Vanilla .....) 30 Jun 2023, 07:19
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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?

Question asks us:

Probability of selecting candy that is ATLEAST green OR Vanilla

Here it is easy to find probability of selecting candy that is NEITHER green NOR Vanilla.

Neither Green -
R+B+V by total units - 7/10

Neither Vanilla -
1/2 (given just 2 options)

Neither Green NOR Vanilla - (7/10)*(1/2) = 7/20

Now probability of getting candy that is atleast green OR Vanilla = 1- (7/20) which is 13/20
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Question of the Week- 19 (A store sells equal number of Vanilla .....) 26 Sep 2025, 20:39
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