Question

A number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). The 8 outcomes are listed in the table below. Note that each outcome has the same probability For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. 

Answer 1

a) As odd number on each of the last two rolls. This means that the first roll can still be odd or even. Therefore the outputs here are given as:

= { OOO, EOO }

Therefore, probability = 2/8 = 25
Therefore 0.25 is the required probability here.

b) Alternating odd number and even number,

= {OEO, EOE}

Therefore, probability = 2/8 = 0.25
Therefore 0.25 is the required probability here.

c) Exactly one odd number

= {OEE, EOE, EEO}

Therefore, probability = 3/8 = 0.375
Therefore 0.375 is the required probability here.