A coin is flipped 3 times. Construct a tree diagram to list all the possibilities of the experiment. compute the following probabilities.

Question

a.) the chance of getting 3 tails

b.) the chance of 2 tails

c.) the chance of getting at least 1 tail 

Answer 1

You can use 2ⁿ to figure out the number of possible outcomes where n is the number of tosses.  If n = 3, then there are 8 possible outcomes.  For the tree diagram, the first toss will either be a head or a tail.  The second and third tosses will give you the same choices, but you will have more combinations to deal with.  The sample space will contain the possible combinations of getting heads and tails.

 

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

 

A) P(3 tails) = 1/8 = 0.125

 

B) P(2 tails) = 2/8 = 0.25

 

C) P(at least 1 tail) = 7/8 = 0.875