What is the probability of rolling a total of 7 with a single roll of

Question

What is the probability of rolling a total of 7 with a single roll of two fair six-sided dice, each with the distinct numbers 1 through 6 on each side?

(A) 1/12
(B) 1/6
(C) 2/7
(D) 1/3
(E) 1/2

Celerma · Answer

I go with  answer A.

Die 1 : 1,2,3,4,5,6 and Die 2: 1,2,3,4,5,6

So there are three ways we can get 7 and they are : 1+6, 2+5,3+4. The order does not matter as we are concerned about the sum i.e. 7.

So 3/36 = 1/12.

PiE700 · Answer

Total  sample space  from two fair six-sided dice is 36.
There are six possible ways to be 7 i.e. (1+6), (2+5), (3+4), (4+3), (5+2), (6+1)
So, total probability is 6/36 or 1/6.
 Answer is B.
 
Thanks

Mega1234 · Answer

answer is B , 1/6. just calculate cases = 6. total number of cases= 6x6= 36

kunal555 · Answer

Total number of out comes = 6C1*6C1= 36
We can get a sum of 7 with following sets of number 
(1,6)(6,1)(2,5)(5,2)(3,4)(4,3)

There are 6 such sets
So, probability will be 6/36 = 1/6

Answer:-B

amansiwach79 · Answer

Answer is B. If we considered the probability of the first dice as 1 since any no would have a corresponding no from the other dice to add up to 7.
And the second dice P=1/6
hence the probability = 1x1/6=1/6

Would this be a correct approach?

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bhaskar438 · Answer

This can be easily done with the stars and bar method. See: how-many-positive-integers-less-than-10-000-are-there-in-85291.html#p639156 The question asks for a sum of 7 between two dice. Since each die has to have a minimum of 1, there will be 5 stars and 1 bar. ***|** can be arranged in \frac{6!}{5!} = 6 ways. There is a total of 6^2 outcomes, so the answer to this question is \frac{6}{6^2} = answer choice B If the question asked to find the probability of rolling a total of 8 with a single roll of two fair six-sided dice, each with the distinct numbers 1 through 6 on each side. Since each die has to have a minimum of 2, there will be 4 stars and 1 bar. **|** can be arranged in \frac{5!}{4!} = 5 ways. There is a total of 6^2 outcomes, so the answer to this question is \frac{5}{6^2} If the question asked to find the probability of rolling a total of 15 with a single roll of three fair six-sided dice, each with the distinct numbers 1 through 6 on each side, by symmetry it is equivalent to the probability of rolling a total of 6 with a single roll of three fair six-sided dice. Since each die has to have a minimum of 1, there will be 3 stars and 2 bars. *|**| can be arranged in \frac{5!}{2!3!} = 10 ways. There is a total of 6^3 outcomes, so the answer to this question is \frac{10}{6^3} If the question asked to find the probability of rolling a total of 10 with a single roll of three fair six-sided dice, each with the distinct numbers 1 through 6 on each side, you have to be a little careful. First arrange 7 stars and 2 bars, which can be arranged in 9C2 = 36 ways. But these 36 ways are including (1,1,8), which can be arranged in 3 ways and (1,2,7), which can be arranged in 6 ways. After subtracting 9 from 36, the answer to this question becomes \frac{27}{6^3}

BrentGMATPrepNow · Answer

Another approach:
Name the dice "die1" and "die2"
Now recognize that the value appearing on die1 is somewhat  inconsequential , since the value of die2 will determine whether or not the sum is 7. 
To clarify, for ANY value of die1, there is a unique value that die2 can have that will create a sum of 7. 
For example, if die1 = 2, then the sum will equal 7 if die2 = 5
If die1 = 6, then the sum will equal 7 if die2 = 1
If die1 = 1, then the sum will equal 7 if die2 = 6
And so on.

Notice that for any given value of die1, there is ONE value of die2 that will create a sum of 7. In other words, of the  6  possible values of die2, only  1  will create a sum of 7

So, P(sum is 7) = P(die1 has ANY value   AND   die2 creates a sum of 7 with die1)
= P(die1 has ANY value)    X   P(die2 creates a sum of 7 with die1)
= 1    X     1/6 
= 1/6
= B

Cheers,
Brent

Bunuel · Answer

KAPLAN OFFICIAL SOLUTION:

When confronted with a probability question, always remember two points. First, probability is just desired outcomes divided by possible outcomes, so you will need to find this ratio. Second, if more than one event occurs, "and" means multiply and "or" means add.

In this problem, we want to roll a combined 7. We can accomplish this in a number of ways. We can roll a 1 with our first die and a 6 with our second, a 2 first and a 5 second, a 3 first and a 4 second, a 4 first and a 3 second, a 5 first and a 2 second, or a 6 first and a 1 second.

This gives us a total of 6 desired outcomes. Next, we will need to find our possible outcomes. Since we have 6 possible outcomes for the first die and 6 possible outcomes for the second die we should multiply 6 x 6 = 36 possible outcomes. Also note, that this is an "and" situation - we roll the first AND second die - so we want to multiply rather than add.

Finally, we put desired outcomes over possible outcomes, to get 6/36 as the probability of rolling a combined 7. 6/36 simplifies to 1/6, which is  answer (B) .

bumpbot · Answer

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What is the probability of rolling a total of 7 with a single roll of

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