onsider the following.(a) Draw a tree diagram to display all the possible head-tail sequences that can occur when you flip a coin three times. (b) How many sequences contain exactly two heads?(c) Probability extension: Assuming the sequences are all equally likely, what is the probability that you will get exactly two heads when you toss a coin three times? (Round your answer to three decimal places.)
Question
onsider the following.(a) Draw a tree diagram to display all the possible head-tail sequences that can occur when you flip a coin three times. (b) How many sequences contain exactly two heads?(c) Probability extension: Assuming the sequences are all equally likely, what is the probability that you will get exactly two heads when you toss a coin three times? (Round your answer to three decimal places.)
Solution
(a) A tree diagram for flipping a coin three times would look like this:
First Flip: H, T
Second Flip: HH, HT, TH, TT
Third Flip: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
(b) The sequences that contain exactly two heads are: HHT, HTH, THH. So, there are 3 sequences.
(c) The probability of getting exactly two heads when you toss a coin three times is the number of successful outcomes (getting two heads) divided by the total number of outcomes.
There are 8 possible outcomes when flipping a coin three times (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT) and 3 of these outcomes are successful (HHT, HTH, THH).
So, the probability is 3/8 = 0.375 when rounded to three decimal places.
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