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Two dice, each with six sides numbered 1 through 6, are toss

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by BTGmoderatorDC » Thu Dec 20, 2018 1:19 am

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Two dice, each with six sides numbered 1 through 6, are tossed. What is the probability that both dice will come up with either a 1 or a 2 ?


A. 1/36

B. 1/18

C. 1/9

D. 1/3

E. 2/3

OA C

Source: Princeton Review
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Two dice, each with six sides number

by fskilnik@GMATH » Thu Dec 20, 2018 1:41 am
BTGmoderatorDC wrote:Two FAIR dice, each with six sides numbered 1 through 6, are tossed. What is the probability that EACH dice will come up with either a 1 or a 2 ?


A. 1/36

B. 1/18

C. 1/9

D. 1/3

E. 2/3
Source: Princeton Review
$$?\,\,:\,\,{\rm{prob}}\,\,{\rm{just}}\,\,1,2$$
$$\left( {{1^{{\rm{st}}}},\,\,{2^{{\rm{nd}}}}} \right)\,\,\,\,\left\{ \matrix{
\,{\rm{total}}\,\,\,:\,\,6 \cdot 6\,\,{\rm{equiprobable}}\,\, \hfill \cr
\,{\rm{favor}}\,\,:\,\,4\,\,\left[ {\left( {1,1} \right),\left( {1,2} \right),\left( {2,1} \right),\left( {2,2} \right)} \right] \hfill \cr} \right.$$
$$? = {4 \over {6 \cdot 6}} = {1 \over 9}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
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by Brent@GMATPrepNow » Thu Dec 20, 2018 6:34 am
BTGmoderatorDC wrote:Two dice, each with six sides numbered 1 through 6, are tossed. What is the probability that both dice will come up with either a 1 or a 2 ?


A. 1/36

B. 1/18

C. 1/9

D. 1/3

E. 2/3
P(both dice will come up with either a 1 or a 2) = P(1st die is 1 or 2 AND 2nd die is 1 or 2)
= P(1st die is 1 or 2) x P(2nd die is 1 or 2)
= 2/6 x 2/6
= 1/3 x 1/3
= 1/9

Answer: C

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Brent
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by Scott@TargetTestPrep » Wed Feb 27, 2019 9:11 am
BTGmoderatorDC wrote:Two dice, each with six sides numbered 1 through 6, are tossed. What is the probability that both dice will come up with either a 1 or a 2 ?


A. 1/36

B. 1/18

C. 1/9

D. 1/3

E. 2/3

OA C

Source: Princeton Review
Since each die has 6 outcomes, there are a total of 6 x 6 = 36 outcomes when two dice are rolled.

Of these 36 outcomes, (1, 1), (1, 2), (2, 1) and (2, 2) are the only ones in which both dice show either a 1 or a 2. Therefore, the probability is 4/36 = 1/9.

Answer: C

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