Simon is rolling two fair dice. He thinks the probability of getting two sixes is #1/36#. Is this correct and why or why not?

3 Answers
Jun 15, 2017

#"correct"#

Explanation:

#"the probability of obtaining a 6 is"#

#P(6)=1/6#

#"to obtain the probability of getting 2 sixes multiply the"#
#"probability of each outcome"#

#"6 AND 6 " =1/6xx1/6=1/36#

Jun 15, 2017

#1/36# is correct

Explanation:

There are 6 different outcomes on each die. Each outcome on one die can be combined with each outcome on the other.

This means there are #6xx6=36# different possibilities.

However, there is only one way of getting two sixes.

So the probability of double #6# is #color(red)(1/36)#

This is shown in the table below.

#color(blue)(" "1" "2" "3" "4" "5" "6)#

#color(blue)(1):" "2" "3" "4" "5" "6" "7#

#color(blue)(2):" "3" "4" "5" "6" "7" "8#

#color(blue)(3):" "4" "5" "6" "7" "8" "9#

#color(blue)(4):" "5" "6" "7" "8" "9" "10#

#color(blue)(5):" "6" "7" "8" "9" "10" "11#

#color(blue)(6):" "7" "8" "9" "10" "11" "color(red)(12)#

Jun 16, 2017

He is correct.

Explanation:

Let's look at just one die for now. The probability for getting a #6# on one die is #1/6# since there are #6# sides to a die, each number from #1# to #6# occupying a side. The other die is also the same, with numbers #1# to #6# occupying one side of the die. This also means that the probability of rolling a #6# on the second die is also #1/6#. Combined, the probability that you roll a #6# on both dies is

#1/6*1/6=1/36#

This means that Simon is correct.