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# A certain tin contains exactly 10 identically shaped gumdrops, of whic

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Math Expert
Joined: 02 Sep 2009
Posts: 56251
A certain tin contains exactly 10 identically shaped gumdrops, of whic  [#permalink]

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14 Aug 2018, 02:22
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Difficulty:

25% (medium)

Question Stats:

77% (01:20) correct 23% (01:19) wrong based on 67 sessions

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

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Re: A certain tin contains exactly 10 identically shaped gumdrops, of whic  [#permalink]

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20 Aug 2018, 02:01
5
1
if we simplify question, its simply asking that what is the probability of selecting a pair out of 5 pairs?
favorable outcome/total outcome--->5C1/10C2 = 5/45= 1/9...C is the answer
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Joined: 20 Feb 2015
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Concentration: Strategy, General Management
Re: A certain tin contains exactly 10 identically shaped gumdrops, of whic  [#permalink]

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14 Aug 2018, 02:32
1
Bunuel 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. $$\frac{2}{5}$$

no of ways to select the 1st gumdrop =10
no of ways to select the second gumdrop=1

required probability=10*1/10*9=1/9
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Re: A certain tin contains exactly 10 identically shaped gumdrops, of whic  [#permalink]

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14 Aug 2018, 02:39
2
1
1
selecting first gumdrop 2/10 = 1/5
selecting second gumdrop 1/9
so total probability of first event = 1/5 * 1/9 = 1/45
now there are 5 identical event which yield probability 1/45, so,
total probability = 6*1/45 = 1/9
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Re: A certain tin contains exactly 10 identically shaped gumdrops, of whic  [#permalink]

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20 Aug 2018, 02:32
Bunuel 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. $$\frac{2}{5}$$

This question can be solved by using logic:

Once the first gum-drop has been selected, in order to select the second gumdrop(with the same
flavor as the first), one could choose only 1 of the gumdrop from the remaining 9 gumdrops.

Therefore, the probability that the second gumdrop is of the same flavor as the first is $$\frac{1}{9}$$ (Option C)
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Re: A certain tin contains exactly 10 identically shaped gumdrops, of whic   [#permalink] 20 Aug 2018, 02:32
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