Download 12.5 Classwork

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12.5 Classwork: Tree Diagram
1. If two states are selected at random from the 50 states, use the counting principle to determine the
number of possible outcomes if the states are selected
a. With replacement
b. Without replacement
2. A bag contains six batteries, all of which are the same size and are equally likely to be selected. Each
battery is a different brand. If you select three batteries at random, use the counting principle to
determine how many points will be in the sample space if the batteries are selected
a. With replacement
b. Without replacement
Use the counting principle to determine the answer to part (a). Assume that each event is equally likely to
occur.
3. Two coins are tossed.
a. Determine the number of points in the sample space.
b. Construct a tree diagram and list the sample space.
Find the probability that
c. No heads are tossed.
d. Exactly one head is tossed.
e. Two heads are tossed.
4. A box contains three cards. On one card there is a circle. On another card there is a square and on the
third card there is a triangle. Two cards are selected at random with replacement.
a. Determine the number of points in the sample space.
b. Construct a tree diagram and determine the sample space.
Find the probability that
c. Two circles are selected.
d. A square and then a triangle are selected.
e. At least one circle is selected.
5. Three coins are tossed.
a. Determine the number of points in the sample space.
b. Construct a tree diagram and list the sample space.
Find the probability that
c. No heads are tossed.
d. Exactly one head is tossed.
e. Three heads are tossed.
6. Two dice are rolled.
a. Determine the number of points in the sample space.
b. Construct a tree diagram and list the sample space.
Find the probability that
c. A double (a 1, 1, or 2, 2, etc.) is rolled.
d. A sum of 7 is rolled.
e. A sum of 2 is rolled.
f. Are you as likely to roll a sum of 2 as you are of rolling a sumo f 7? Explain your answer.
7. Three different people are to be selected at random, and each will be given one gift certificate. There is
one certificate from Home Depot, one from Sears, and one from Outback Steakhouse. The first person
selected gets to choose one of the certificates. The second person selected gets to choose between the
two remaining certificates. The third person selected gets the third certificate.
a. Determine the number of points in the sample space.
b. Construct a tree diagram and determine the sample space.
Find the probability that
c. Sears is selected first.
d. Home Depot is selected first and Outback Steakhouse is selected second.
e. The certificates are selected in this order: Sears, Outback Steakhouse, Home Depot.