Three people are being selected at random, each will be given one gift card.
There is one card from Home Depot,one from Best Buy and one from Red Lobster. The first person selected will get to choose between the two remaining cards. The third person selected gets the third card.
a) Determine the number of points in the sample space.
b) construct a tree diagram and determine the sample space.
Determine the probability that
a) the best buy card is selected first
b)the home depot card is selected first and the red lobster card is selected last
c)the cards are selected in this order best buy, red lobster, home depot
a) To determine the number of points in the sample space, we need to consider all possible combinations of the three cards being given to the three people. Since the first person has three options, the second person has two options, and the third person receives the last remaining card, we multiply these numbers together.
Total number of points in the sample space = 3 (options for the first person) * 2 (options for the second person) * 1 (option for the third person) = 6
Therefore, the sample space consists of 6 possible outcomes.
b) To construct a tree diagram and determine the sample space, we start by drawing three branches from the top representing the three options for the first person – Best Buy, Home Depot, and Red Lobster. From each of these branches, we draw two more branches representing the options for the second person, and from each of these branches, we draw one more branch representing the option for the third person.
The tree diagram would look like this:
Best Buy Home Depot Red Lobster
/ \ / \ / \
Home Depot Red Lobster Best Buy Red Lobster Best Buy Home Depot
The sample space consists of all the possible paths through the tree diagram, which are the outcomes of the different options for each person.
c) To determine the probability of specific events, we need to count the number of favorable outcomes and divide it by the total number of outcomes.
a) Probability that the Best Buy card is selected first:
In this case, there is only one favorable outcome – Best Buy being selected first. And since we have already determined that there are 6 possible outcomes in the sample space, the probability is:
P(Best Buy selected first) = 1/6
b) Probability that Home Depot card is selected first and Red Lobster card is selected last:
In this case, the favorable outcome is Home Depot being selected first and Red Lobster being selected last. From the tree diagram, we can see that there is only one path that satisfies this outcome. Therefore, the probability is:
P(Home Depot selected first and Red Lobster selected last) = 1/6
c) Probability that the cards are selected in the order Best Buy, Red Lobster, Home Depot:
Again, the favorable outcome is the specific ordering of the cards. From the tree diagram, we can see that there is only one path that satisfies this outcome as well. Therefore, the probability is:
P(Best Buy, Red Lobster, Home Depot) = 1/6