Question

You flip a coin 3 times, use a tree diagram to determine the sample space of the experiment and use it to answer the following questions.

a) In how many ways can you get exactly 2 tails?



b) In how many ways can you get at least 1 tail?



c) In how many ways can you get greater than 3 heads?



d) In how many ways can you get less than 1 head?

Answer 1

Answer and explanation:

The sample space of flipping a coin 3 times can be represented using a tree diagram. Here is the tree diagram for this experiment:

H

/ \

/ \

H T

/ \ / \

H T H T

Copy

a) To get exactly 2 tails, you can get either HHT, HTH, or THH. So, there are 3 ways to get exactly 2 tails.

b) To get at least 1 tail, you can get either HTT, THT, THH, HTH, TTH, HTH, or TTT. So, there are 7 ways to get at least 1 tail.

c) To get greater than 3 heads, you can’t get more than 3 heads because there are only 3 flips. So, there are 0 ways to get greater than 3 heads.

d) To get less than 1 head (i.e., no heads), you can only get TTT. So, there is only 1 way to get less than 1 head.