Suppose a fair coin is tossed three times.

Question

Suppose a fair coin is tossed three times.

a) Using a tree diagram, list out all outcomes in the sample space. Let TT denote the coin lands on tails and HH denote the coin lands on heads. 

 

b) Using the sample space found in part (a), what is the probability of getting exactly 1 tail or no more than 1 head. 

c) If the first toss is a tail, what is the probability of getting at least two tails? Hint: What is the new sample space? Use the tree diagram from part (a) 

Answer 1

a.) Here is the sample space: HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

The tree has 3 nodes (one for each toss). The sample space is represented by each branch of the tree.

Total ways => 8

b.) Ways to get exactly one tail: HHT, HTH, THH ==> 3 ways

Ways to get no more than one head: TTT, TTH,THT, HTT ==> 4 ways

P = (3+4)/8 = 7/8

c.) You can just look at 2 tosses. New sample space: TT, HH, TH, HT

Since you already have one tail, you can now just look at the probability of at least one tail from the new sample space:

P = 3/4