4. (a) If a coin is tossed independently 100 times and the probability of getting a heads is p = 0.5, what is the probability of getting k \"Heads\"? What are the most likely values for the numbers of heads whose total probability is at least 95%? Compute this range exactly (which will require a numerical computation). This is the set of values for the number of heads we would need to observe to test if the coin was fair a level of signicance of 5%. Repeat this for the case of p = 0.49. If p = 0.49, what is the chance that the admittedly unfair coin (since p 71$ 0.5) would pass the test that it is a fair coin at the 5% level of signicance? Do not make any approximations