Two standard dice are rolled, what is the probability of rolling a pair (both the same number)?

Question

Anthony Amato · Accepted Answer

The probability of rolling the pair

#P(E)=1/6~~0.17#

We note that, if a die is rolled the sample space: #S={1,2,3,4,5,6}# We know that ,if two dice rolled the sample space : #S={1,2,3,4,5,6}xx{1,2,3,4,5,6}# #:.S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),# #color(white)(...............)(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),# #color(white)(...............)(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),# #color(white)(...............)(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),# #color(white)(...............)(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),# #color(white)(...............)(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}# i.e. When two dice are tossed together , the possible pairs are : #color(blue)(n=6xx6=36# Let ,event #E=#the same number on both dice. #=> E={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}# #=>#no. of comeout pair #color(blue)( r=6# So , the probability of rolling the pair #=P(E)=r/n# #=>P(E)=6/36# #=>P(E)=1/6~~0.17#

Quinn Allen · Answer

#1/6#

Since we are rolling two six-sided dice, there are #6xx6#, or #36# different possibilities. This will be our denominator.

How many ways can we get double numbers?

#{1,1}, {2,2}, {3,3}, {4,4}, {5,5}, {6,6}#

We have #6# different ways of getting double numbers. This is our numerator.

Thus, the probability of rolling pairs is #6/36# or

#1/6#

Hope this helps!

Audrey Andrews · Answer

undefined The probability of rolling a pair (both the same number) with two standard dice is $ \frac{1}{6} $.