Question

When throwing fair dice, all six faces of each die are equally likely. there are thirty-six total possible outcomes (any of the six faces of die a can be matched with any of the six faces of die b). what is the probability the sum of the pips (spots) on the two faces is at least 9?

Answer 1

Probability of sum of pips on two faces is at least 9 =
`(5)/(18)`

Explanation:

Experiment: Throwing two fair dice.

Total no of Outcome =
`6^2` = 36

Sample space (list of outcome) is attached.

Let E be the event that sum of pips on two faces is at least 9.

`Probability \:(\,Event \:E\,)\: =\;(No.\: of\: favorable\: outcome\:of\: Event\: E)/(Total\: No.\: of \:Outcome)`

Favorable outcome are where sum is 9 , 10 , 11 and 12.

From Sample space, No. of Favorable outcome = 10

∴
`Prob\: (\: E\: ) = (10)/(36)`

`Prob\: (\: E\: ) = (5)/(18)`