Suppose kitty tosses a coin 6 times. What is the probability that she counts more "heads" than tails?
This is a question from the test and I got only partial marks so I am wondering what is the solution to this.
What I did was I assume the number of coin outcomes,for example: hhhhhh,tttttt,and so on and I use the formula P(E) = n(E)/n(S)
where n(E) is the number of events n that has heads more than tails.
Best Answer
The probability of getting the exact same number of heads and tails is ${^6{\rm C}_3}\cdot\tfrac 1{2^6} = \frac 5{16}$
Due to symmetry then, the probability of seeing more heads than tails is $\tfrac 12\big(1-\tfrac 5{16}\big)$, that's $\color{green}{\tfrac {11}{32}}$. This is also the probability of seeing less heads than tails.
Assuming, that is, that the coins are unbiased.
$$\dfrac {11}{32}$$