Which events are not independent?
A. You toss three coins and get one head and one tail.
B. You choose three different ice toppings for a sundae.
C. You draw two colored pencils without replacement and get one red and one yellow.
D. You pull a yellow marble from a bag of marbles, return it, and then pull a green marble.
C and D are not independent events.
Is it C or D?
Both events C and D are not independent.
I can only choose one.
If you can only choose one, then event D is not independent because it involves drawing marbles with replacement. The outcome of the first draw affects the probability of the second draw. Therefore, D is not an independent event.
On Friday nights the local diner serves three main entrees, each with a choice of vegetables. The entrees are beef, chicken, and fish. The vegetables are spinach, broccoli, and carrots. How many possible diners (entrees and vegetable combinations) does the diner serve? List them.
There are 3 possible entrees and 3 possible vegetable choices for each entree. Therefore, there are 3 x 3 = 9 possible combinations of entrees and vegetables.
The possible diners are:
1. Beef with spinach
2. Beef with broccoli
3. Beef with carrots
4. Chicken with spinach
5. Chicken with broccoli
6. Chicken with carrots
7. Fish with spinach
8. Fish with broccoli
9. Fish with carrots
Marissa is researching information about martial arts students. She found that 7 out of 12 martial artists practice every day. There are 144 martial arts students at a school.
a. Predict how many students practice every day.
b. What is the sample size?
a. We can use the proportion 7/12 to make a prediction for the entire population. If we assume that the proportion of students who practice every day is the same for the entire population, we can set up the following proportion:
(7/12) = x/144
We can cross-multiply and solve for x:
12x = 7 * 144
x = (7 * 144) / 12
x = 84
Therefore, we predict that approximately 84 students out of 144 practice every day.
b. The sample size is 12, as the proportion 7/12 is based on a sample of 12 martial artists. The total number of martial arts students at the school (144) is the population size.
To determine which events are not independent, we need to consider whether the outcome of one event affects the probability of the other event occurring.
A. In this scenario, tossing three coins and getting one head and one tail are independent events. The outcome of one coin toss does not influence the outcome of the other coin tosses.
B. Choosing three different ice toppings for a sundae is also an independent event. The choice of one topping does not impact the availability or choice of the other toppings.
C. Drawing two colored pencils without replacement and getting one red and one yellow is a dependent event. The outcome of the first draw affects the probability of the second draw. If you draw a red pencil first, there will be one less red pencil remaining for the second draw, changing the probability of drawing a red pencil again.
D. Pulling a yellow marble from a bag of marbles, returning it, and then pulling a green marble is an independent event. Returning the yellow marble resets the probability distribution for the second draw, making it independent of the first draw.
Therefore, the events that are not independent are:
C. Drawing two colored pencils without replacement and getting one red and one yellow.
It is important to understand the concept of independence and dependent events to analyze various situations correctly.