3. A fair coin is tossed 3 times. (a) How many events are there in the sample sp

Question

3. A fair coin is tossed 3 times. (a) How many events are there in the sample space (i.e. total number of possible outcomes)? What are they? List them. Use "H" for heads and "T" for tails. You may use a tree diagram if it is helpful (b) What is the probability of getting exactly one head in 3 tosses? (c) What is the probability of getting exactly two heads in 3 tosses? (d) What is the probability of getting at least two heads in 3 tosses? (e) What is the probability of getting no heads in 3 tosses?

Explanation / Answer

Answer to the question is as follows:

a. Total events in sample space = 2*2*2 = 8 = {HHH, TTT, THH, THT, HTT, HTH, TTH, HHT}

b. P(getting exactly 1 H) = {HTT,THT, TTH } P(exactly 1 H) = 3/8

c. P(getting 2 heads in 3 tosses) = {HTH, HHT, THH} , P(exactly 2 heads) = 3/8

d. P(getting atleast 2 heads in 3 tosses) = {{HTH, HHT, THH, HHH} = 4/8 = 1/2

e. P( no heads in 3 tosses) = {TTT} out of 8: P(no heads in 3 tosses) = 1/8

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