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
For the second question the answer is b.
what about the first question @Anonymous Human
1st question:
The events that are not independent are:
- You toss three coins and get one head and one tail. This is because the outcome of each coin toss is dependent on the outcome of the other coin tosses.
- You draw two colored pencils without replacement and get one red and one yellow. This is because the probability of drawing the second colored pencil depends on the outcome of the first draw.
2nd question:
The probability that the coin shows heads and the number cube shows 5 is 1/12. This is because the probability of the coin showing heads is 1/2, and the probability of the number cube showing 5 is 1/6. To find the probability of both events occurring, you multiply the individual probabilities (1/2 * 1/6 = 1/12).
To determine which events are not independent, we need to check if the occurrence of one event affects the probability of the other event.
1st question:
Let's analyze each situation:
- Tossing three coins and getting one head and one tail: In this case, the events of getting a head and getting a tail are not independent because the outcome of one coin toss affects the other two coin tosses. To determine the probability, we can use the concept of combinations. There are three possible outcomes when tossing three coins: HHH, HHT, and HTT. The probability of getting one head and one tail would be 2/3.
- Choosing three different ice toppings for a sundae: In this situation, the events are independent. The choice of one topping does not affect the probabilities of choosing the other toppings. Each choice is independent, so the probability is the product of the probabilities for each topping choice.
- Drawing two colored pencils without replacement and getting one red and one yellow: The events in this scenario are also not independent since the first choice affects the possibilities for the second choice. To find the probability, we take the number of favorable outcomes and divide it by the total number of possible outcomes.
- Pulling a yellow marble from a bag of marbles, returning it, and then pulling a green marble: In this case, the events are independent because the marble is replaced back into the bag after each draw. The probability of pulling a yellow marble and then a green marble can be calculated by multiplying the probabilities of each event.
2nd question:
The probability that the coin shows heads and the number cube shows 5 can be calculated by multiplying the probability of each event. Assuming the coin and number cube are fair and independent:
- The probability of the coin showing heads is 1/2 (since there are two equally likely outcomes: heads or tails).
- The probability of the number cube showing 5 is 1/6 (since the number cube has six equally likely outcomes: 1, 2, 3, 4, 5, or 6).
To find the probability of both events occurring, we multiply the probabilities: 1/2 * 1/6 = 1/12. Therefore, the probability that the coin shows heads and the number cube shows 5 is 1/12.