##### Example on Probability | MIT Assignment

Bob has a peculiar four sided die.When he rolls the dice, the probability of any particular outcome is proportional to the sum of the results of each die. All outcomes that result in a particular sum are equally likely.

A) What is the probability of the sum being even?

B) What is the probability of Bob rolling a 2 and a 3, in any order?

The easiest way to solve this problem is to make a table of some sort, similar to the one below.

 Die 1 Die 2 Sum P(Sum) 1 1 2 2p 1 2 3 3p 1 3 4 4p 1 4 5 5p 2 1 3 3p 2 2 4 4p 2 3 5 5p 2 4 6 6p 3 1 4 4p 3 2 5 5p 3 3 6 6p 3 4 7 7p 4 1 5 5p 4 2 6 6p 4 3 7 7p 4 4 8 8p Total 80p

P(All outcomes) = 80p (Total from the table)

=> p = $1 \over 80$

A) P(Even Sum) = ( 2p + 4p + 4p + 6p+ 4p + 6p + 6p + 8p )= 40p = ${1 \over 2}$

B) P(Rolling a 2 and a 3) = P(2,3) + P(3,2)  = 5p + 5p = 10p =  $1 \over 8$

##### 1Comment
Mukesh
1 Oct 2017 06:13 pm

where is it given that we have two dice or we throw the dice twice?