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?

Answer

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 @mukeshkumar440
1 Oct 2017 06:13 pm

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