1. Which of the following are independent events? (3 points)
((** is my answer))
A. Flipping a coin and rolling a number cube**
B. Choosing two marbles without replacement
C. Spinning a spinner twice**
D. Choosing a card, replacing it and then choosing another card**
2. A bag holds 3 blue marbles, 5 red marbles, and 2 green marbles. Find the probability of choosing a red marble and then a green marble with replacement
A. 1/10**
B. 1/2
C. 1/9
D. 1/5
3 part A. A cooler at a soccer game holds ten apple juices and ten orange juices. If the first player chooses a juice and drinks it, then the second player chooses a juice, what if the probability that both players will get orange juice?
A. 1/20**
B. 9/38
C.1/4
D. 1/400
3 part b. If the first player picks a juice but returns it without opening it, and a second player picks a juice, what is the probability that both players would choose orange juice?
A. 1/4**
B. 1/2
C. 1/10
D. 1/100
Please help me with this, and these are just guesses so idk if they are correct
1. Wouldn't where the spinner stops the first time effect the second spin?
2. 5/10 * 2/10 = 10/100 = 1/10
3. Disagree. 10/20 * (10-1)/(20-1) = ?
4. Agree
1. Flipping a coin and rolling a number cube, Spinning a spinner twice, Choosing a card, replacing it and then choosing another card
2. 1/10
3. 9/38
4. 1/4
1. A. Flipping a coin and rolling a number cube - Independent events, as the outcome of one does not affect the outcome of the other.
B. Choosing two marbles without replacement - Not independent, as the outcome of the first draw affects the outcome of the second draw.
C. Spinning a spinner twice - Independent events, as the outcome of one spin does not affect the outcome of the other.
D. Choosing a card, replacing it, and then choosing another card - Independent events, as replacing the card restores the original probabilities for the second draw.
2. The probability of choosing a red marble and then a green marble with replacement can be calculated as follows:
P(red marble) = 5/10 = 1/2
P(green marble) = 2/10 = 1/5
Since the events are independent, the probability of both events occurring is obtained by multiplying the individual probabilities:
P(red marble and green marble) = P(red marble) * P(green marble) = (1/2) * (1/5) = 1/10
Therefore, the correct answer is A. 1/10.
3a. The probability that both players will get orange juice can be calculated as follows:
P(first player gets orange juice) = 10/20 = 1/2
P(second player gets orange juice) = 9/19 (after the first player has chosen an orange juice, there are 9 orange juices left out of the remaining 19 juices)
Since the events are independent, the probability of both events occurring is obtained by multiplying the individual probabilities:
P(both players get orange juice) = P(first player gets orange juice) * P(second player gets orange juice) = (1/2) * (9/19) = 9/38
Therefore, the correct answer is B. 9/38.
3b. If the first player picks a juice but returns it without opening it, and a second player picks a juice, the probability that both players choose orange juice remains the same as in part a.
P(both players choose orange juice) = 9/38
Therefore, the correct answer is B. 1/2 is not correct for this scenario.
Hope that helps, and if you have any more questions, feel free to ask!
1. To determine which events are independent, we need to understand the concept of independent events. Two events are considered independent if the outcome of one event has no influence on the outcome of the other event. Let's analyze each option:
A. Flipping a coin and rolling a number cube: These events are independent because the outcome of flipping a coin (getting heads or tails) does not impact the outcome of rolling a number cube (getting any number).
B. Choosing two marbles without replacement: These events are dependent since the first marble chosen affects the number and type of marbles remaining for the second selection.
C. Spinning a spinner twice: These events are independent since the outcome of the first spin does not affect the outcome of the second spin. The spinner is presumed to be reset after each spin.
D. Choosing a card, replacing it, and then choosing another card: These events are independent since the card is replaced before choosing the second card. The first card's selection does not impact the deck's composition for selecting the second card.
Based on this analysis, the correct answers for independent events are Option A (flipping a coin and rolling a number cube) and Option C (spinning a spinner twice).
2. In this situation, we need to find the probability of choosing a red marble and then a green marble, assuming replacement after each selection.
The total number of marbles in the bag is 3 (blue) + 5 (red) + 2 (green) = 10. Since replacement is allowed, the probability of choosing a red marble on the first draw is 5/10 = 1/2. After replacing the red marble, the probability of choosing a green marble on the second draw is also 2/10 = 1/5.
To find the overall probability, we multiply the probabilities of the two events: (1/2) * (1/5) = 1/10. Therefore, the correct answer is A. 1/10.
3 part A. Since there are 10 orange juices out of a total of 20 juices, the probability that the first player chooses an orange juice is 10/20 = 1/2. After the first player chooses, there are now 19 juices left, including 9 orange juices. So, the probability that the second player chooses an orange juice is 9/19.
To find the probability of both players choosing orange juice, we multiply the probabilities: (1/2) * (9/19) = 9/38. Therefore, the correct answer is B. 9/38.
3 part B. In this case, the first player picks a juice but returns it without opening it. This means that the initial number and composition of the juices remains the same. So, the probability that the first player chooses an orange juice is still 10/20 = 1/2.
After the first player's choice, there are still 10 orange juices out of a total of 20 juices. Therefore, the probability that the second player chooses an orange juice is still 10/20 = 1/2.
To find the probability of both players choosing orange juice, we multiply the probabilities: (1/2) * (1/2) = 1/4. Therefore, the correct answer is A. 1/4.
I hope this helps clarify the answers for you! Let me know if you have any further questions.
#1. ok
#2. ok
#3a. 10/20 * 9/19
#3b. ok