Question

a. Suppose that a fair coin is tossed 15 times. If 10 heads are observed, determine an expression /
equation for the probability that 7 heads occurred in the first 9 tosses.

b. Now, generalize your result from part a. Now suppose that a fair coin is to be tossed n times. If x
heads are observed in the n tosses, derive an expression for the probability that there were y heads
observed in the first m tosses. Note the following restrictions: y ≤ x, and m ≤ n. [2]

c. Identify the probability distribution for the random variable Y, where Y represents the number of
heads observed in the first m tosses, given that there were x heads observed in a total of n tosses. Be sure
to state the range for the random variable Y. [4]

d. Does your result in part c. require that the coin be fair? Explain / justify your answer. [2]

Answer 1