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
Two dice, each with six sides numbered 1 through 6, are toss
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- fskilnik@GMATH
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$$?\,\,:\,\,{\rm{prob}}\,\,{\rm{just}}\,\,1,2$$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
$$\left( {{1^{{\rm{st}}}},\,\,{2^{{\rm{nd}}}}} \right)\,\,\,\,\left\{ \matrix{
\,{\rm{total}}\,\,\,:\,\,6 \cdot 6\,\,{\rm{equiprobable}}\,\, \hfill \cr
\,{\rm{favor}}\,\,:\,\,4\,\,\left[ {\left( {1,1} \right),\left( {1,2} \right),\left( {2,1} \right),\left( {2,2} \right)} \right] \hfill \cr} \right.$$
$$? = {4 \over {6 \cdot 6}} = {1 \over 9}$$
This solution follows the notations and rationale taught in the GMATH method.
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Fabio.
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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)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(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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Since each die has 6 outcomes, there are a total of 6 x 6 = 36 outcomes when two dice are rolled.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
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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