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

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

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

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