Question

Suppose that I flip a fair coin 34 times. What is the probability that it will land on heads exactly 19 times?

Make sure your answer is between 0 and 1.

Answer 1

Given, a fair coin is flipped 34 times.

Let X denote the total number of heads that have turned up in the 34 trials.

Since, the coin is fair so the chances of getting a head on each flip is,p=0.5

X follows a binomial distribution with parameters 34 and 0.5

The probability mass function of X is given by :

                                                  $P(X=x)=\binom{34}{x}(0.5)^{34}$        x=0,1,2,.............,34

The probability of getting exactly 19 heads is given by P(X=19)

                                                   $P(X=19)=\binom{34}{19}(0.5)^{34}$

                                                                            $=34!/(19!*(34-19)!)*0.5^{34}$

                                                                            $=0.10803$