Consider 2 weighted coins, C1 and C2. For C1, the probability of heads is 0.8 and for C2, the probability of heads is 0.2. That isp(C1=H)=0.8 andp(C2=H)=0.2.

a. What is the expected number of heads on two consecutive tosses ofC1?

b. Let f(N) be the probability ofNconsecutive head tosses ofC1. What is the lowest value ofN(N>1) such thatf(N) < 0.5?

c. What is the probability that the coins give the same result (both heads or both tails)?

d. What is the probability that C2 GIVEN THAT C1 and C2 give different results? that is, calculatep(C2=T |C1C2). (express your answer to a precision within 3 places beyond the decimal point).