Which events are NOT independent?
1.You toss three coins and get one head and one tail.
2.You choose three different ice toppings for a sundae.
3.You draw two colored pencils without replacement and get one red and one yellow.
4.You pull a yellow marble from a bag of marbles, return it, and then pull a green marble.
wow three years and no one answered. thats stoopy
The events that are NOT independent are:
3. You draw two colored pencils without replacement and get one red and one yellow.
4. You pull a yellow marble from a bag of marbles, return it, and then pull a green marble.
In both of these situations, the outcome of the first event affects the probability of the second event.
To determine which events are not independent, we need to understand the concept of independence. Two events are considered independent if the outcome of one event does not affect the outcome of another event. If the events are not independent, it means the outcome of one event does affect the outcome of the other event.
Now, let's analyze each scenario:
1. You toss three coins and get one head and one tail.
In this scenario, the outcome of the first coin toss (head or tail) does not affect the outcome of the subsequent coin tosses. So, the events are independent.
2. You choose three different ice toppings for a sundae.
In this scenario, choosing one ice topping does not impact the availability or choice of the next ice topping. So, the events are independent.
3. You draw two colored pencils without replacement and get one red and one yellow.
In this scenario, after drawing one colored pencil (e.g., red), the available pool of colored pencils changes, which impacts the probability of drawing a different color (e.g., yellow) on the second draw. Hence, the events are dependent.
4. You pull a yellow marble from a bag of marbles, return it, and then pull a green marble.
In this scenario, returning the yellow marble to the bag restores the original pool of marbles, making the probability of drawing a green marble unaffected by the previous outcome. Therefore, the events are independent.
Based on this analysis, the events that are NOT independent are the third scenario (drawing two colored pencils without replacement) and the fourth scenario (pulling a yellow marble, returning it, and then pulling a green marble).