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A fair coin is tossed four times and a person win Rs.1 for each head and lose Rs.1.50 for each tail that turns up.From the sample space,calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts.

$\begin{array}{1 1}(A)\;4,1.50,-1.00,-3.50,-6.00,P=\large\frac{1}{16},\frac{1}{4},\frac{3}{8},\frac{1}{4},\frac{1}{16}\\(B)\;3,1.00,1.00,3.50,6.00,P=\large\frac{1}{14},\frac{1}{8},\frac{3}{4},\frac{1}{4},\frac{1}{9}\\(C)\;-4,-1.50,1.00,3.50,6.00,P=\large\frac{1}{15},\frac{1}{14},\frac{5}{8},\frac{1}{8},\frac{1}{15}\\(D)\;\text{None of these}\end{array} $

1 Answer

Given a coin is tossed four times
$\therefore$ Possible outcomes =$2^4=16$
$\therefore$ Sample space can be written as
Sample space =HHHH,Amount =1+1+1+1=4
Sample space =HHHT,Amount =1+1+1-1.50=3-1.50=1.50
Sample space =HHTH,Amount =1+1-1.50+1=1.50
Sample space =HHTT,Amount =1+1-1.50-1.50=-1.00
Sample space =HTHH,Amount =1-1.50+1+1=1.50
Sample space =HTHT,Amount =1-1.50+1-1.50=-1.00
Sample space =HTTH,Amount =1-1.50-1.50+1=-1.00
Sample space =HTTT,Amount =1-1.50-1.50-1.50=-3.50
Sample space =THHH,Amount =-1.50+1+1+1=1.50
Sample space =THHT,Amount =-1.50+1+1-1.50=-1.00
Sample space =THTH,Amount =-1.50+1-1.50+1=-1.00
Sample space =THTT,Amount =-1.50+1-1.50-1.50=-3.50
Sample space =TTHH,Amount =-1.50-1.50+1+1=-1.00
Sample space =TTHT,Amount =-1.50-1.50+1-1.50=-3.50
Sample space =TTTH,Amount =-1.50-1.50-1.50+1=-3.50
Sample space =TTTT,Amount =-1.50-1.50-1.50-1.50=-6
Therefore from the samples we get 5 type of different amounts.
$4,1.50,-1.00,-3.50,-6.00$
4 has occurred 1 time
1.50 has occurred 4 times
-1.00 has occurred 6 times
-3.50 has occurred 4 times
-6.00 has occurred 1 time
$\Rightarrow$ P(winning of Rs.4.00)=$\large\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$
$\Rightarrow \large\frac{1}{16}$
$\Rightarrow$P(winning of Rs1.50)=$\large\frac{4}{16}=\frac{1}{4}$
$\Rightarrow$P(winning of Rs-1.00)=$\large\frac{6}{16}=\frac{3}{8}$
$\Rightarrow$P(winning of Rs-3.50)=$\large\frac{4}{16}=\frac{1}{4}$
$\Rightarrow$P(winning of Rs-6.00)=$\large\frac{1}{16}$
Hence (A) is the correct answer.
answered Jul 1, 2014 by sreemathi.v
 

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