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# A certain tin contains exactly 10 identically shaped gumdrop

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A certain tin contains exactly 10 identically shaped gumdrop [#permalink]  11 Aug 2018, 09:44
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68% (00:55) correct 32% (00:58) wrong based on 25 sessions
A certain tin contains exactly 10 identically shaped gumdrops, of which 2 are cherry, 2 are lemon, 2 are grape, 2 are cinnamon and 2 are strawberry. If 2 gumdrops are randomly selected, one at a time and without replacement, what is the probability that the second gumdrop is the same flavor as the first?

A. $$\frac{1}{45}$$

B. $$\frac{1}{25}$$

C. $$\frac{1}{9}$$

D. $$\frac{1}{5}$$

E. $$\frac{2}{5}$$
[Reveal] Spoiler: OA

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Re: A certain tin contains exactly 10 identically shaped gumdrop [#permalink]  11 Aug 2018, 10:03
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Carcass wrote:
A certain tin contains exactly 10 identically shaped gumdrops, of which 2 are cherry, 2 are lemon, 2 are grape, 2 are cinnamon and 2 are strawberry. If 2 gumdrops are randomly selected, one at a time and without replacement, what is the probability that the second gumdrop is the same flavor as the first?

A. $$\frac{1}{45}$$

B. $$\frac{1}{25}$$

C. $$\frac{1}{9}$$

D. $$\frac{1}{5}$$

E. $$\frac{2}{5}$$

Here,
for the first draw we pick any gumdrop,

Now we have remaining 9 gumdrop and selection a matching flavor with the first one = $$\frac{1}{9}$$
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Re: A certain tin contains exactly 10 identically shaped gumdrop [#permalink]  24 Nov 2018, 06:01
We also need to calculate the probability of selecting the 1st gumdrop , which will be 1/5 for any gumdeop and then multiply the probability of selecting the 2nd gumdrop , which should be 1/9.
To make it clear would you have also ignored the probability of selecting the 1st gumdrop if the numbers would have been different ?
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Re: A certain tin contains exactly 10 identically shaped gumdrop [#permalink]  24 Nov 2018, 06:31
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Expert's post
kunalkmr62 wrote:
We also need to calculate the probability of selecting the 1st gumdrop , which will be 1/5 for any gumdeop and then multiply the probability of selecting the 2nd gumdrop , which should be 1/9.
To make it clear would you have also ignored the probability of selecting the 1st gumdrop if the numbers would have been different ?

No...

You can choose any of the first so 10/10, the second has to be a pair of this so1/9
Total 10/10*(1/9)=1/9..

If we take the way you have taken..
Then you are calculating ways to pick up a specific gumdeop..
So (2/10)*(1/9)...
But the one you choose can be any of five so 5C1..
So 5C1*(1/5)(1/9)=5*(1/5)(1/9)=1/9
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: A certain tin contains exactly 10 identically shaped gumdrop   [#permalink] 24 Nov 2018, 06:31
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