Answer to Question #253528 in Statistics and Probability for Shaon

Question

1.    There is an experiment of flipping a fair coin 100 times. Let H denote the number of heads from this experiment. (4 points)

a.    Calculate the probabilities of H= 40, 50.

b.    Draw a frequency graph of H in (a).

 

2.    Suppose a fair coin is tossed until a head comes up for the first time. (6 points.)

a.    Calculate the probability that the experiment ends on the first trial.

b.    Calculate the probability that the experiment on the third trial.

c.    Calculate the probability that the experiment ends on an even-numbered toss.

Answer 1

1.

a.

$P(H=40) = C^{100}_{40} (\frac{1}{2})^{40} (\frac{1}{2})^{60} = 0.0108 \\ P(H=50) = C^{100}_{50} (\frac{1}{2})^{50} (\frac{1}{2})^{50} = 0.0796$

b.

2.

a. P(ends on the first trial) $= \frac{1}{2} = 0.5$

b. P( nds on the third trial) $= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8} = 0.125$

c. P(ends on an even-numbered toss) $= (\frac{1}{2})^2 + (\frac{1}{2})^4 + (\frac{1}{2})^6+...+(\frac{1}{2})^{2n}$