Which events are not independent?
You toss three coins and get one head and one tail.
You choose three different ice toppings for a sundae.
You draw to colored pencils without replacement and get one red and yellow.
You pull a yellow marble from a bag of marbles, returns it, and then pull a green marble.
How can you "toss three coins and get one head and one tail"?
It said it in the question. Idk if they accidentally messed the question up or meant it.
In the given scenarios, the events that are not independent are:
1. You draw two colored pencils without replacement and get one red and yellow.
This is not an independent event because the outcome of drawing the second colored pencil depends on the outcome of drawing the first colored pencil. Since the first colored pencil drawn is already determined to be red, the probability of drawing a yellow colored pencil as the second one will be affected.
2. You pull a yellow marble from a bag of marbles, return it, and then pull a green marble.
This is an independent event since you return the yellow marble to the bag before pulling the green marble. Each marble pull is not influenced by the previous outcome, as the bag is considered to be "reset" after each pull.
The other two scenarios, tossing three coins and choosing three different ice toppings for a sundae, involve independent events because the outcomes of these events do not affect each other.
To determine which events are not independent, we need to look at the definition of independence. Two events are considered independent if the outcome of one event does not affect the outcome of the other event. So, let's analyze each scenario:
1. Tossing three coins and getting one head and one tail: In this case, the outcome of each coin toss is independent of the other tosses. For example, if you toss the first coin and get a head, it does not affect the outcome of the second or third coin toss. Therefore, the events in this scenario are independent.
2. Choosing three different ice toppings for a sundae: In this scenario, the outcome of choosing each topping may depend on the choices made previously. For instance, if you choose a chocolate syrup topping first, it may impact your decision on the next topping to ensure a complementary flavor. Therefore, the events in this scenario are not independent.
3. Drawing two colored pencils without replacement and getting one red and one yellow: When drawing without replacement, the outcome of the second draw is influenced by the outcome of the first draw. For example, if you draw a red pencil first, there is one less red pencil remaining for the second draw, affecting the probability of drawing a red pencil again. Hence, the events in this scenario are not independent.
4. Pulling a yellow marble from a bag of marbles, returning it, and then pulling a green marble: In this scenario, returning the yellow marble means that the probability of drawing a green marble is unaffected by the previous outcome. Returning the marble reinstates the initial probabilities for all colors. Therefore, the events in this scenario are independent.
To summarize, the events that are not independent are choosing three different ice toppings for a sundae and drawing two colored pencils without replacement and getting one red and one yellow.