I'm having a hard time with this question, but I did the best that I could. I would appreciate any help to correctly solve it.
Suppose that a coin is tossed three times and the side that lands up is noted. For instance, HHT indicates that the coin landed with a head up on the first two tosses and a tail up on the third.
a) List all the possible outcomes of the sample space. b) Write each of the following events as a set and find its probability. i) exactly one toss results in a head ii) at least two tosses result in a head iii) the event that no head is obtained. c) What is the probability that exactly two tosses were heads if we know that there was a head on the first toss? d) What is the probability that exactly two heads were tosses if we know that at least one of the tosses was a head?
A) 3 tosses and each toss has 2 possibilities, so: 2^3= 8 possibilities
HHH, TTT, HTH, HTT, HHT, THT, THH, TTH
B) (i) 1/8 = 12.5% (ii) 2/8 = 1/4 = 25% (iii) 1/8 = 12.5%
C) 1/8= 12.5%
D) 4/8 = 1/2 = 50% (The wording on this question is hard to decipher)