Question

You asked your $3$ friends Marie, Dennis and Jack to toss a fair coin $12$ times each in a row and the outcomes of this experiment is given as below:

Coin Tossed by	Number of heads	Number of Tails
Marie	7	5
Dennis	6	6
Jack	8	4

Calculate the probability of occurence of heads for each individual.

• A. Marie $=\frac{5}{12}$
  
  Dennis $=\frac{1}{2}$
  
  Jack $=\frac{1}{3}$
  
• B. Marie $=\frac{7}{12}$
  
  Dennis $=\frac{1}{2}$
  
  Jack $=\frac{2}{3}$
  
• C. Marie $=\frac{5}{12}$
  
  Dennis $=\frac{1}{2}$
  
  Jack $=\frac{2}{3}$
  
• D. Marie $=\frac{7}{12}$
  
  Dennis $=\frac{1}{2}$
  
  Jack $=\frac{1}{3}$
  

Answer 1

The correct option is B Marie $=\frac{7}{12}$


Dennis $=\frac{1}{2}$

Jack $=\frac{2}{3}$

Let $\text{P(H)}$ denotes the probability of occurrence of head when a coin is tossed.
$\text{P(H)}=\frac{\text{Number of times head appears}}{\text{Number of total trials}}$

For Marie,
Out of $12$ trials, head appears $7$ times.
The probability of occurence of head for Marie:
$\text{P(H)}=\frac{7}{12}$


For Dennis,
Out of $12$ trials, head appears $6$ times.
The probability of occurence of head for Dennis:
$\text{P(H)}=\frac{6}{12}$

$\text{P(H)}=\frac{1}{2}$


For Jack,
Out of $12$ trials, head appears $8$ times.
The probability of occurence of head for Jack:
$\text{P(H)}=\frac{8}{12}$

$\text{P(H)}=\frac{2}{3}$


Therefore, option (b.) is the correct answer.