What will be the sample space if a six sided dice, a seven sided dice, and two coins are
thrown together? What is the probability of getting two heads and the sum of the dice to
be 12?
Answers
Given : a six sided dice, a seven sided dice, and two coins are thrown together
To Find : Sample space
probability of getting two heads and the sum of the dice to be 12
Solution:
a six sided dice, = 6 possible out comes { 1 , 2 , 3 , 4 , 5 , 6 }
a 7 sided dice, = 7 possible out comes { 1 ,2 ,3 , 4 , 5 , 6 , 7 }
two coins = 2 x 2 = 4 possible out comes { HH , HT , TH , TT}
Total possible out comes = 6 x 7 x 4 = 168
S = { {1 , 1 , HH) , (1 , 1 , HT ) , (1 , 1 , TH ) , ( 1 , 1 , TT) ,
{1 , 2 , HH) , (1 , 2 , HT ) , (1 , 2 , TH ) , ( 1 , 2 , TT) ,
{1 , 3 , HH) , (1 , 3 , HT ) , (1 , 3 , TH ) , ( 1 , 3 , TT) ,
{1 , 4 , HH) , (1 , 4 , HT ) , (1 , 4 , TH ) , ( 1 , 4 , TT) ,
{1 , 5 , HH) , (1 , 5, HT ) , (1 , 5 , TH ) , ( 1 , 5 , TT) ,
{1 , 6 , HH) , (1 , 6 , HT ) , (1 , 6 , TH ) , ( 1 , 6 , TT) ,
{1 , 7 , HH) , (1 , 7 , HT ) , (1 , 7 , TH ) , ( 1 , 7 , TT) ,
{2 , 1 , HH) , (2 , 1 , HT ) , (2 , 1 , TH ) , ( 2 , 1 , TT) ,
{2 , 2 , HH) , (2 , 2 , HT ) , (2 , 2 , TH ) , ( 2 , 2 , TT) ,
{2, 3 , HH) , (2 , 3 , HT ) , (2 , 3 , TH ) , ( 2 , 3 , TT) ,
{2 , 4 , HH) , (2 , 4 , HT ) , (2 , 4 , TH ) , (2 , 4 , TT) ,
{2, 5 , HH) , (2 , 5, HT ) , (2 , 5 , TH ) , ( 2 , 5 , TT) ,
{2 , 6 , HH) , (2, 6 , HT ) , (2 , 6 , TH ) , ( 2 , 6 , TT) ,
{2 , 7 , HH) , (2 , 7 , HT ) , (2 , 7 , TH ) , ( 2 , 7 , TT) ,
{3 , 1 , HH) , (3 , 1 , HT ) , (3 , 1 , TH ) , ( 3 , 1 , TT) ,
{3 , 2 , HH) , (3 , 2 , HT ) , (3, 2 , TH ) , (3 , 2 , TT) ,
{3, 3 , HH) , (3 , 3 , HT ) , (3, 3 , TH ) , ( 3 , 3 , TT) ,
{3 , 4 , HH) , (3 , 4 , HT ) , (3 , 4 , TH ) , ( 3 , 4 , TT) ,
{3, 5 , HH) , (3 , 5, HT ) , (3 , 5 , TH ) , (3 , 5 , TT) ,
{3 , 6 , HH) , (3, 6 , HT ) , (3 , 6 , TH ) , ( 3 , 6 , TT) ,
{3 , 7 , HH) , (3 , 7 , HT ) , (3 , 7 , TH ) , ( 3 , 7 , TT) ,
{4 , 1 , HH) , (4 , 1 , HT ) , (4 , 1 , TH ) , ( 4 , 1 , TT) ,
{4 , 2 , HH) , (4 , 2 , HT ) , (4, 2 , TH ) , (4 , 2 , TT) ,
{4, 3 , HH) , (4 , 3 , HT ) , (4, 3 , TH ) , ( 4 , 3 , TT) ,
{4 , 4 , HH) , (4 , 4 , HT ) , (4 , 4 , TH ) , ( 4 , 4 , TT) ,
{4, 5 , HH) , (4 , 5, HT ) , (4 , 5 , TH ) , (4 , 5 , TT) ,
{4 , 6 , HH) , (4, 6 , HT ) , (4 , 6 , TH ) , ( 4 , 6 , TT) ,
{4 , 7 , HH) , (4 , 7 , HT ) , (4 , 7 , TH ) , ( 4 , 7 , TT) ,
{5 , 1 , HH) , (5 , 1 , HT ) , (5 , 1 , TH ) , ( 5 , 1 , TT) ,
{5 , 2 , HH) , (5 , 2 , HT ) , (5, 2 , TH ) , (5 , 2 , TT) ,
{5, 3 , HH) , (5 , 3 , HT ) , (5, 3 , TH ) , ( 5 , 3 , TT) ,
{5 , 4 , HH) , (5 , 4 , HT ) , (5 , 4 , TH ) , ( 5 , 4 , TT) ,
{5, 5 , HH) , (5 , 5, HT ) , (5 , 5 , TH ) , (5 , 5 , TT) ,
{5 , 6 , HH) , (5, 6 , HT ) , (5 , 6 , TH ) , ( 5 , 6 , TT) ,
{5 , 7 , HH) , (5 , 7 , HT ) , (5 , 7 , TH ) , ( 5 , 7 , TT) ,
{6 , 1 , HH) , (6 , 1 , HT ) , (6 , 1 , TH ) , ( 6 , 1 , TT) ,
{6 , 2 , HH) , (6 , 2 , HT ) , (6, 2 , TH ) , (6 , 2 , TT) ,
{6, 3 , HH) , (6 , 3 , HT ) , (6, 3 , TH ) , ( 6 , 3 , TT) ,
{6 , 4 , HH) , (6 , 4 , HT ) , (6 , 4 , TH ) , ( 6 , 4 , TT) ,
{6, 5 , HH) , (6 , 5, HT ) , (6 , 5 , TH ) , (6 , 5 , TT) ,
{6 , 6 , HH) , (6, 6 , HT ) , (6 , 6 , TH ) , ( 6 , 6 , TT) ,
{6 , 7 , HH) , (6, 7 , HT ) , (6 , 7 , TH ) , ( 6 , 7 , TT) }
Getting two heads and sum 12
{ 5 , 7 , H, H} } , { 6 , 6, H , H }
Probability = 2/168 = 1/84
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