Two identical six-sided dice are rolled. What is the probability that

Question

Two identical six-sided dice are rolled. What is the probability that the sum of the dice will be at least 5?

A. 1/36
B. 1/6
C. 1/3
D. 5/6
E. 35/36

Sreesha9758 · Answer

Answer is D

1-(6/36)=30/36=5/6

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viv007 · Answer

Probability of getting sum atlest 3 = 1 - proba of getting 1 and prob of getting 2..
Since two dice rolled so prob of 1 is 0 
Prob of sum getting 2 = 1/6*1/6 = 1/36

Prob of getting sum atlst 3 is = 1-1/36
 = 35/36
Answer E

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pushpitkc · Answer

When two identical six-sided dice are rolled, in order for the sum to be less than 5,
the various combinations are (1,1),(1,2),(2,2),(2,1),(1,3),(3,1) - 6 combinations

The total possibilities are 6*6 = 36

Probability(Atleast 5) = 1 - P(Sum less than 5) =  1 - \frac{6}{36} = \frac{30}{36} = \frac{5}{6}

Hence, the probability that the sum of the dice will be atleast 5 is  \frac{5}{6}  (Option D)

PolarisTestPrep · Answer

Hello!

Let's start with some probability basics.

Probability = Number of desired outcomes/Total number of possible outcomes

Because of this, probability is always between 0 and 1

The total number of possible outcome in rolling dice is 36

That is because there are 6 possible outcomes in the first die, and six possible outcomes for the second die.

Therefore there are 6 x 6 = 36 total possible outcomes

If we were to ask what is the probability of getting a picture of a cat on both dice, the probability is 0 because there are 0 outcomes that will feature a cat, unfortunately, out of the 36 possible outcomes

\frac{0}{36}  = 0

If we were to ask what is the probability of getting a number from a roll of dice, that probability is 1 because there are 36 different ways to get a number out of the 36 possible outcomes of rolling dice. That is to say, all of the possible outcomes will result in a number. The probability is 1 meaning it is 100% a sure thing

\frac{36}{36}  = 1

This question asks what the probability is of the sum of the dice being 5 or higher

Now if we start to think of the possible combinations

1 2
2 3
4 2
4 1
5 1
6 3
3 5

We can see that many add up to 5 or larger, so it is more useful to see how many rolls add up to less than 5 and subtract that number from the total number of rolls

Let's see:

1 1
1 2
1 3
2 1
2 2
3 1

There are 6 different rolls that will add up to less than 5

This is out of 36 total possible rolls

36 - 6 = 30 of the possible rolls will add up to 5 or larger

\frac{30}{36 }  =  \frac{5}{6}

The answer is (D)

MathRevolution · Answer

Two dice : 6 * 6 = 36 outcome

Sum at least 5 = 1 - sum less than 5

Sum less than 5 :

=> (1,1) (1,2), (1,3) = 3 results
=> (2,1) , (2, 2) = 2 results
=> (3,1) = 1 results

Sum less than 5 probability:  \frac{6}{36} = \frac{1}{6}

Sum at least 5 =  1 - \frac{1}{6} = \frac{5}{6}

Answer D

BrushMyQuant · Answer

Given that Two identical six-sided dice are rolled and we need to find What is the probability that the sum of the dice will be at least 5?

As we are rolling two dice => Number of cases =  6^2  = 36

Out of these 36 outcomes if we are able to find the number of outcomes in which sum is less than 5 and subtract that from 36 then we will get the number of outcomes where we have sum at least 5

Following are the cases in which sum will be less than 5
(1,1), (1,2), (1,3)
(2,1), (2,2)
(3,1)

=> 6 cases

=> 36 - 6 = 30 cases have sum at least 5

=> Probability that Sum of two dice will be at least 5 =  \frac{30}{36}  =  \frac{5}{6}

So,  Answer will be D 
Hope it helps!

Playlist on Solved Problems on Probability  here

Watch the following video to MASTER Dice Rolling Probability Problems

https://www.youtube.com/watch?v=5PVZYQXet18

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