Two coins are tossed 100 times and the following results wer

Two coins are tossed 100 times and the following results were obtained:
Number of Heads : 0;1;2 Number of times Occurred: 10;40;50

Test at a = 0.05 if the coins are fair

Solution

Using a binomial distribution, the probabilities of 0, 1, and 2 heads out of 2 fair coins is

P(0) = 0.25
P(1) = 0.50
P(2) = 0.25

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
10   25   9  
40   50   2  
50   25   25  

          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    36      
          
As df = a - 1,           
          
a =    3      
df = a - 1 =    2      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      
chi^2(crit) =    5.991464547      
          
Also, the p value is          
          
p =    1.523E-08      
          
Thus, comparing chi^2 and chi^2(crit) [or, p and significance level], we   REJECT THE NULL HYPOTHESIS.  

Thus, there is a significant evidence that the coin is not fair. [CONCLUSION]