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
You wording is confusing me.
You say, 3 people are chosen at random, then each is given a gift card
What group are the 3 people chosen from ?
You say, "The first person selected will get to choose between the two remaining cards" . What happened to the first card?
Then, "The third person selected gets the third card
What happened to the second person?
Would it just be:
the first person gets to pick a card
the second person get to pick a card
the third person gets the remaining card ?
In an experiment, each of two people has six cards labeled 1 through 6. The first person chooses a card from set one while the second person chooses a card from set two. What is the probability that the two people will choose the same card. Write your answer as a percent, rounded to the nearest whole number
a) To determine the number of points in the sample space, we need to consider the possible outcomes for each selection.
The first person selected has three options: Home Depot, Best Buy, or Red Lobster card.
The second person selected has two options (since one card has been chosen by the first person), and will receive the card not chosen by the first person.
The third person selected will receive the last remaining card.
So, the number of points in the sample space is:
3 (choices for the first person) * 2 (choices for the second person) * 1 (choice for the third person) = 6
b) To construct a tree diagram, we can start by listing the possible outcomes for each selection:
1st person: {Home Depot, Best Buy, Red Lobster}
2nd person: {Remaining two cards not chosen by 1st person}
3rd person: {Remaining card}
Here is the tree diagram representation:
/ | \
HD BB RL
| | |
HD RL BB
| | |
RL BB RL
The sample space shown in the tree diagram consists of all the possible outcomes:
{HD, RL, BB} {HD, BB, RL} {BB, HD, RL} {BB, RL, HD} {RL, HD, BB} {RL, BB, HD}
c) To determine the probabilities, we need to count the favorable outcomes and divide by the total number of points in the sample space.
a) Probability that the Best Buy card is selected first:
There are two favorable outcomes: {BB, HD, RL} and {BB, RL, HD}.
So, the probability is: 2/6 = 1/3 or approximately 0.3333.
b) Probability that the Home Depot card is selected first and the Red Lobster card is selected last:
There is only one favorable outcome: {HD, RL, BB}.
So, the probability is: 1/6 or approximately 0.1667.
c) Probability that the cards are selected in the order Best Buy, Red Lobster, Home Depot:
There is only one favorable outcome: {BB, RL, HD}.
So, the probability is: 1/6 or approximately 0.1667.