The two dice are tossed. What is the probably of the event that the sum of two numbers on the both dice at least equal 6 and at most equal 9?

1 Answer
Jan 22, 2016

P_("["6,9"]")=5/9

Explanation:

With out loss of generality we can assume one die is color(red)("red") and the second die is color(green)("green")

For each of the color(red)(6) faces on the color(red)("red die") there are color(green)(6) different possible outcomes on the color(green)("green die").
rArr there are color(red)(6) xx color(green)(6) = color(blue)(36) possible combined outcomes.

Of these outcomes

A total of 6 can be achieved in color(cyan)(5) ways:{(color(red)(1),color(green)(5)),(color(red)(2),color(green)(4)),(color(red)(3),color(green)(3)),(color(red)(4),color(green)(2)),(color(red)(5),color(green)(1))}

A total of 7 can be achieved in color(cyan)(6) ways:{(color(red)(1),color(green)(6)),(color(red)(2),color(green)(5)),(color(red)(3),color(green)(4)),(color(red)(4),color(green)(3)),(color(red)(5),color(green)(2)),(color(red)(6),color(green)(1))}

A total of 8 can be achieved in color(cyan)(5) ways:{(color(red)(2),color(green)(6)),(color(red)(3),color(green)(5)),(color(red)(4),color(green)(4)),(color(red)(5),color(green)(3)),(color(red)(6),color(green)(2))}

A total of 9 can be achieved in color(cyan)(4) ways:{(color(red)(3),color(green)(6)),(color(red)(4),color(green)(5)),(color(red)(5),color(green)(4)),(color(red)(6),color(green)(3))}

Since these event are mutually exclusive there are
color(white)("XXX")color(cyan)(5+6+5+4) =color(brown)(20) ways of achieving {6,7,8,9}

So the probability of achieving in{6,7,8,9}is
color(white)("XXX")color(brown)(20)/color(blue)(36)= 4/9