Consider the experiment in which a person rolls two fair dice. (a) How many outc
ID: 3219032 • Letter: C
Question
Consider the experiment in which a person rolls two fair dice.
(a) How many outcomes are in the sample space S of this experiment?
(b) Find the probability P(E) of the following event: E = {The English words for the numbers rolled start with the same letter.}
(c) Let R be the following event: R = {The numbers rolled are distinct, and the Russian words for these numbers start with the same letter.}
(d) Using what we know from part (c), find the probability P(T) of the following event:
T = {The Russian words for the numbers rolled start with the same letter.}
Explanation / Answer
a) S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}=36 outcomes.
b) E={(1,1),(2,2),(2,3),(3,2),(3,3),(4,4),(4,5),(5,4),(5,5),(6,6)}=10/36
c) R={(4,5),(5,4)}=2/36
d) R={(1,1),(2,2),(3,3),(4,4),(4,5),(5,4),(5,5),(6,6)}=8/36