1st question:
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.
2nd question:
A coin is tossed and a number cube is rolled. What is the probability that the coin shows heads and the number cube shows 5?
1/6
1/12
2/3
1/4
John?
B is 1/6
The first one is I think D. Pulling out a yellow marble, putting it back and then pulling out a green one.
1st question:
Hmm, well, let's see which events are not independent here:
- You toss three coins and get one head and one tail: This event is not independent because the outcome of each coin toss can affect the outcome of the others.
- You choose three different ice toppings for a sundae: This event is independent because the choice of ice toppings does not affect each other.
- You draw two colored pencils without replacement and get one red and yellow: This event is not independent because once you draw the first pencil, it affects the probability of drawing a specific color for the second pencil.
- You pull a yellow marble from a bag of marbles, return it, and then pull a green marble: This event is independent since you return the yellow marble to the bag, so the probability of pulling a green marble is not affected by the first draw.
2nd question:
The probability that the coin shows heads and the number cube shows 5 is the product of the probabilities of each event happening:
Probability of getting heads on a coin toss: 1/2
Probability of rolling a 5 on a number cube: 1/6
So, the probability is (1/2) * (1/6) = 1/12.
An adorable little 1/12 chance! So, good luck! I hope that helps!
1st question:
To determine which events are not independent, we need to understand the definition of independent events. Two events are considered independent if the outcome of one event does not affect the outcome of the other event.
Let's analyze each scenario to determine if the events are independent or not:
1. Tossing three coins and getting one head and one tail: The outcome of each coin toss is independent of the others, so this event is independent.
2. Choosing three different ice toppings for a sundae: Since each topping choice is separate and doesn't depend on the previous choices, this event is also independent.
3. Drawing two colored pencils without replacement and getting one red and one yellow: In this scenario, the outcome of the second draw is dependent on the first draw because there are fewer pencils available. Therefore, this event is not independent.
4. Pulling a yellow marble from a bag of marbles, returning it, and then pulling a green marble: In this case, since the marble is returned after the first pull, the outcome of the second pull is independent of the first. Therefore, this event is independent.
Based on the analysis, the events that are not independent are in scenario 3, where the colored pencil draws without replacement result in one red and one yellow.
2nd question:
To find the probability that the coin shows heads and the number cube shows 5, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The number of favorable outcomes is 1 (coin showing heads and number cube showing 5).
The total number of possible outcomes when tossing a coin and rolling a number cube is 2 (for the coin) multiplied by 6 (for the number cube), which is 12.
So, the probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes:
1/12
Therefore, the correct answer is 1/12.
You confused me with the first question. Tossed three coins, but only two results??
If you post your answers, someone will check them.