7. Which of the following is an example of independent events?
A rolling two number cubes
B selecting marbles from a bag without
replacement after each draw
C choosing and eating a piece of candy from a dish and then choosing another piece of candy***
D Pulling a card from a deck when other players have already pulled several cards from that deck
8. A bag of fruit contains 4 apples, 1 plum, 2 apricots, and 3 oranges. Pieces of fruit are drawn twice with replacement. What is P(apple, then
apricot)? (1 point)
a 4/5
b 2/25
c 3/25***
d 3/5
9. A coin is flipped three times. How the does P(H, H, H) compare to P(H, T, H)? (1 point)
A. P(H, H, H) is greater than P(H, T, H)
B.P(H, T, H) is greater than P(H, H, H).
c.The probabilities are the same.***
d.There is no way to tell with the information given.
10. A coin is tossed and a number cube is rolled. What is P(heads, a number less than 5)? (1 point)
A 1/3***
B 5/12
C 2/3***
D 5/6
im stuck help me
Sure, I can help you. Let's go through each question step-by-step.
7. Which of the following is an example of independent events?
The correct answer is C. choosing and eating a piece of candy from a dish and then choosing another piece of candy. Independent events are events where the outcome of one event does not affect the outcome of another event.
8. A bag of fruit contains 4 apples, 1 plum, 2 apricots, and 3 oranges. Pieces of fruit are drawn twice with replacement. What is P(apple, then apricot)?
To calculate the probability, we need to consider that the fruit is drawn with replacement, which means that after each draw, the fruit is placed back into the bag.
The probability of drawing an apple is 4/10 (4 apples out of 10 total fruits), and the probability of drawing an apricot is 2/10 (2 apricots out of 10 total fruits).
Since the events are independent and occur one after another, we need to multiply the probabilities:
P(apple, then apricot) = (4/10) * (2/10) = 8/100 = 2/25
So the answer is b. 2/25.
9. A coin is flipped three times. How does P(H, H, H) compare to P(H, T, H)?
To compare the two probabilities, we need to consider that each coin flip is independent and has a 50% chance of being heads (H) or tails (T).
P(H, H, H) = (1/2) * (1/2) * (1/2) = 1/8
P(H, T, H) = (1/2) * (1/2) * (1/2) = 1/8
Therefore, the probabilities are the same, so the answer is c. The probabilities are the same.
10. A coin is tossed, and a number cube is rolled. What is P(heads, a number less than 5)?
To calculate the probability, we need to consider that the coin toss and number cube roll are independent events.
The probability of getting heads on the coin toss is 1/2, and the probability of getting a number less than 5 on the number cube is 4/6.
Since the events are independent, we multiply the probabilities:
P(heads, a number less than 5) = (1/2) * (4/6) = 4/12 = 1/3
So the answer is A. 1/3.
I hope this helps you! Let me know if you have any further questions.
Sure, I can help you with that! Let's go through each question one by one:
7. The independent events are events that do not affect each other. In this case, choosing and eating a piece of candy from a dish and then choosing another piece of candy is an example of independent events, as the outcome of the first choice does not influence the outcome of the second choice.
8. To find the probability of drawing an apple first and then an apricot (with replacement), we need to calculate the probability of drawing an apple (4/10) and the probability of drawing an apricot (2/10). Since we are drawing with replacement, the probabilities remain the same for both draws. To find the combined probability, we multiply the individual probabilities: (4/10) * (2/10) = 8/100 = 2/25. Therefore, the correct answer is option c) 3/25.
9. In this case, P(H, H, H) represents the probability of getting three heads in a row when flipping a coin three times. P(H, T, H) represents the probability of getting a head, then a tail, and then another head. Since each flip is independent of the others, the probability of getting a head on the first and third flips is the same, and the probability of getting a tail on the second flip does not influence the probabilities of the other flips. Therefore, the probabilities of P(H, H, H) and P(H, T, H) are the same. The correct answer is option c) The probabilities are the same.
10. To find the probability of getting a heads coin toss and a number less than 5 on the number cube, we need to calculate the individual probabilities. The probability of getting heads on a coin toss is 1/2, and the probability of getting a number less than 5 on a number cube is 4/6 (there are four numbers less than 5: 1, 2, 3, and 4 out of a total of six possible outcomes). To find the combined probability, we multiply the individual probabilities: (1/2) * (4/6) = 4/12 = 1/3. Therefore, the correct answer is option A) 1/3.
I hope this helps! Let me know if you have any more questions.
7. Disagree.
8. If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
4/10 * 2/10 = ?
9. Correct
10. P(heads) = 1/2
P(<5) = P(4 or 3 or 2 or 1)
Either-or probabilities are found by adding the individual probabilities.
1/2 * 4/6 = 4/12 = ?