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# Two dice, each with six sides numbered 1 through 6, are tossed. What

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Math Expert
Joined: 02 Sep 2009
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Two dice, each with six sides numbered 1 through 6, are tossed. What  [#permalink]

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13 Nov 2018, 01:26
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Difficulty:

45% (medium)

Question Stats:

45% (00:57) correct 55% (00:55) wrong based on 132 sessions

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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

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Two dice, each with six sides numbered 1 through 6, are tossed. What  [#permalink]

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Updated on: 20 Dec 2018, 07:48
1
Bunuel 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

either 1 or 2 in first dice : 2/6
Either 1 or 2 in second dice : 2/6

2/6*2/6=1/9 option c
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Originally posted by Archit3110 on 13 Nov 2018, 04:07.
Last edited by Archit3110 on 20 Dec 2018, 07:48, edited 2 times in total.
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Re: Two dice, each with six sides numbered 1 through 6, are tossed. What  [#permalink]

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13 Nov 2018, 09:19
both dice coming up with the number 1 - 1/6*1/6=1/36

both dice coming up with number 2 - 1/6*1/6=1/36

Since it is an 'OR' problem we need to add them both so 1/36+1/36=2/36=1/18

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Two dice, each with six sides numbered 1 through 6, are tossed. What  [#permalink]

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13 Nov 2018, 21:16

Solution

Given:
• Two dice, each with six sides numbered 1 through 6, are tossed

To find:
• The probability that both dice will come up either 1 or 2

Approach and Working:
• P(both 1) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$
• P(both 2) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$
• P( a 1 and a 2) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$
• P( a 2 and a 1) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$

Thus, P( either 1 or 2) = $$\frac{1}{36} + \frac{1}{36} + \frac{1}{36} + \frac{1}{36} = \frac{4}{36} = \frac{1}{9}$$

Hence, the correct answer is Option C

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Re: Two dice, each with six sides numbered 1 through 6, are tossed. What  [#permalink]

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13 Nov 2018, 22:01
EgmatQuantExpert wrote:

Solution

Given:
• Two dice, each with six sides numbered 1 through 6, are tossed

To find:
• The probability that both dice will come up either 1 or 2

Approach and Working:
• P(both 1) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$
• P(both 2) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$
• P( a 1 and a 2) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$
• P( a 2 and a 1) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$

Thus, P( either 1 or 2) = $$\frac{1}{36} + \frac{1}{36} + \frac{1}{36} + \frac{1}{36} = \frac{4}{36} = \frac{1}{9}$$

Hence, the correct answer is Option C

If this is the right answer then I'm afraid but the question hasn't been worded properly. It clearly mentions that the number on both dice should be either a 1 or a 2. That means both the dice should have either 1 or either 2 and not like 1 in the first and 2 in the second one.
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Re: Two dice, each with six sides numbered 1 through 6, are tossed. What  [#permalink]

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14 Nov 2018, 01:04
Shbm wrote:
EgmatQuantExpert wrote:

Solution

Given:
• Two dice, each with six sides numbered 1 through 6, are tossed

To find:
• The probability that both dice will come up either 1 or 2

Approach and Working:
• P(both 1) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$
• P(both 2) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$
• P( a 1 and a 2) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$
• P( a 2 and a 1) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$

Thus, P( either 1 or 2) = $$\frac{1}{36} + \frac{1}{36} + \frac{1}{36} + \frac{1}{36} = \frac{4}{36} = \frac{1}{9}$$

Hence, the correct answer is Option C

If this is the right answer then I'm afraid but the question hasn't been worded properly. It clearly mentions that the number on both dice should be either a 1 or a 2. That means both the dice should have either 1 or either 2 and not like 1 in the first and 2 in the second one.

Shbm : I also got the question wrong , the wording of this question is not clear.
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Re: Two dice, each with six sides numbered 1 through 6, are tossed. What  [#permalink]

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14 Nov 2018, 01:24
Either 1 or 2 means

1,2
2,1
1,1
2,2

So 4/36

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Re: Two dice, each with six sides numbered 1 through 6, are tossed. What  [#permalink]

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14 Nov 2018, 05:58
Archit3110 wrote:
Shbm wrote:
EgmatQuantExpert wrote:

Solution

Given:
• Two dice, each with six sides numbered 1 through 6, are tossed

To find:
• The probability that both dice will come up either 1 or 2

Approach and Working:
• P(both 1) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$
• P(both 2) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$
• P( a 1 and a 2) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$
• P( a 2 and a 1) = $$\frac{1 * 1}{6 * 6} = \frac{1}{36}$$

Thus, P( either 1 or 2) = $$\frac{1}{36} + \frac{1}{36} + \frac{1}{36} + \frac{1}{36} = \frac{4}{36} = \frac{1}{9}$$

Hence, the correct answer is Option C

If this is the right answer then I'm afraid but the question hasn't been worded properly. It clearly mentions that the number on both dice should be either a 1 or a 2. That means both the dice should have either 1 or either 2 and not like 1 in the first and 2 in the second one.

Shbm : I also got the question wrong , the wording of this question is not clear.

yea same for me. However, don't worry such a poorly worded question wouldn't appear on the GMAT.
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Re: Two dice, each with six sides numbered 1 through 6, are tossed. What  [#permalink]

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15 Nov 2018, 19:52
Bunuel 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

Possible Cases:
1,1
1,2
2,1
2,2
Therefore, 4 possible cases.
Total cases = 6 x 6 = 36
Probability = 4/36 = 1/9
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Re: Two dice, each with six sides numbered 1 through 6, are tossed. What  [#permalink]

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20 Dec 2018, 07:43
1
Top Contributor
Bunuel 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

Cheers,
Brent
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Re: Two dice, each with six sides numbered 1 through 6, are tossed. What  [#permalink]

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20 Dec 2018, 15:38
would it be correct to say that each dice has a 1/3 chance of getting a desired number so...

1/3*1/3 = 1/9?
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Re: Two dice, each with six sides numbered 1 through 6, are tossed. What  [#permalink]

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27 Feb 2019, 10:25
1
Bunuel 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

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.

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Re: Two dice, each with six sides numbered 1 through 6, are tossed. What   [#permalink] 27 Feb 2019, 10:25
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