SOLUTION: A fair coin is tossed, and a fair die is thrown. Write down sample spaces for (a) the toss of the coin; (b) the throw of the die; (c) the combination of these experiments. Let A be

Algebra ->  Probability-and-statistics -> SOLUTION: A fair coin is tossed, and a fair die is thrown. Write down sample spaces for (a) the toss of the coin; (b) the throw of the die; (c) the combination of these experiments. Let A be      Log On


   

Question 1197753: A fair coin is tossed, and a fair die is thrown. Write down sample spaces for (a) the toss of the coin; (b) the throw of the die; (c) the combination of these experiments. Let A be the event that a head is tossed, and B be the event that an odd number is thrown. Directly from the sample space, calculate P(A ∩ B) and P(A ∪ B).
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
A fair coin is tossed, and a fair die is thrown. Write down sample spaces for
(a) the toss of the coin;
{H,T}, P(H)=P(T)=1/2
(b) the throw of the die;
{1,2,3,4,5,6}, P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=1/6
(c) the combination of these experiments.
{H&1,H&2,H&3,H&4,H&5,H&6,T&1,T&2,T&3,T&4,T&5,T&6}
P(H&1)=P(H&2)=P(H&3)=P(H&4)=P(H&5)=P(H&6)=
P(T&1)=P(T&2)=P(T&3)=P(T&4)=P(T&5)=P(T&6)=(1/2)(1/6)=1/12
Let A be the event that a head is tossed,
A = {H}
and B be the event that an odd number is thrown.
B = {1,3,5}
Directly from the sample space, calculate P(A ∩ B)
P(A ∩ B) = P(A&B) = P({H}&{1,2,3}) = P[(H&1)&(H&3)&(H&5)] = (1/12)(1/12)(1/12) = (1/12)^3 = 1/1728
and P(A ∪ B)
P(A ∪ B) = P(A and/or B) = P({H} and/or {1,2,3}) = 

[That's all the ones with either an [H or a (1 or 2 or 3)] or both, 
an [H and a (1 or 2 or 3)] 

P({H&1,H&2,H&3,H&4,H&5,H&6,T&1,T&2,T&3}) = P(H&1)+P(H&2)+P(H&3)+P(H&4)+
P(H&5)+P(H&6)+P(T&1)+P(T&2)+P(T&3) = 
(1/12)+(1/12)+(1/12)+(1/12)+(1/12)+(1/12)+(1/12)+(1/12)+(1/12) = 
(1/12)∙9 = 9/12 = 3/4

Edwin