What is the probability of rolling a number greater than or equal to 8 with the sum of two dice, given that at least one of the dice must show a 6?

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Dec 18, 2017

Answer:

#9/11 (Answer D.)#

Explanation:

#P["sum" >= 8|"at least one dice shows 6"]#
#= "P[sum >= 8 AND at least one dice shows 6]" / "P[at least one dice shows 6]"#
#= (9/36) / (1 - (5/6)^2)#
#= (1/4) / (11/36)#
#= 9/11#
#(Answer D.)#

#P["sum>=8 AND at least one dice shows 6"] =#
#"9/36 because there are 9 good combinations out of the 36 :"#
#(6,2),(2,6),(6,3),(3,6),(6,4),(4,6),(6,5),(5,6), and (6,6).#

#P["at least one dice shows 6"] = 1 - P["no dice shows 6"]#
#= 1 - (5/6)^2#
#"Another possibility is using the formula for OR :"#
#"P[dice 1 is 6 OR dice 2 is 6]"#
#"= P[dice 1 is 6] + P[dice 2 is 6] - P[ dice 1 AND dice 2 is 6]"#
#= 1/6 + 1/6 - 1/(6*6)#
#= (6 + 6 - 1)/36#
#= 11/36#

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