1.

P(number < 2) (1 point)

1/6
2/6
4/6
3/6

2.
P(number ≥ 3) (1 point)

4/6
1/6
2/6
5/6

3.
P(complement of 4) (1 point)

1/6
5/6
2/6
4/6

4.
A multiple choice question has 5 possible answers. What are the odds in favor of guessing the right answer? (1 point)

1:5
4:1
1:4
3:2

My answers:
1. 2/6
2. 5/6
3. 4/6
4. 1:5

in #1 - 3 you don't state what the event is, so those questions are incomplete

#4. Odds in favour of some event
= prob of the event / prob of not the event

prob of correct choice = 1/5

so the odds in favour of picking the right answer
= (1/5 / 4/5)
= 1/4
or 1 : 4

Your answers are correct. Here's a step-by-step explanation for each question:

1. P(number < 2):
- There are 6 possible numbers (1, 2, 3, 4, 5, 6).
- Only one number is less than 2, which is 1.
- So, the probability is 1/6.

2. P(number ≥ 3):
- There are 6 possible numbers (1, 2, 3, 4, 5, 6).
- Numbers greater than or equal to 3 are 3, 4, 5, and 6.
- So, the probability is 4/6 or simplified to 2/3.

3. P(complement of 4):
- The complement of an event is the opposite of that event.
- There are 6 possible numbers (1, 2, 3, 4, 5, 6).
- The complement of 4 is all the numbers except 4, which are 1, 2, 3, 5, and 6.
- So, the probability is 5/6.

4. Odds in favor of guessing the right answer:
- When we say "odds in favor of," it means the ratio of successful outcomes to unsuccessful outcomes.
- There is only one correct answer out of 5 possible answers.
- So, the odds in favor of guessing the right answer are 1:5.

To solve these probability problems, we need to understand some basic concepts.

1. P(number < 2): This is asking for the probability of getting a number less than 2. Since the given options are fractions, we can assume that the number is chosen from a set of six numbers (e.g., rolling a fair, six-sided die). To calculate the probability, we need to count the favorable outcomes (numbers less than 2) and divide it by the total number of possible outcomes (all six numbers).

The numbers less than 2 are 1. Since there is only one favorable outcome, the probability is 1/6. Therefore, option 1/6 is the correct answer.

2. P(number ≥ 3): This is asking for the probability of getting a number greater than or equal to 3. Similar to the previous problem, we have six possible outcomes. To calculate the probability, we need to count the favorable outcomes (numbers greater than or equal to 3) and divide it by the total number of possible outcomes.

The numbers greater than or equal to 3 are 3, 4, 5, 6. There are four favorable outcomes, so the probability is 4/6, which simplifies to 2/3. Therefore, option 5/6 is the correct answer.

3. P(complement of 4): The complement of an event is the opposite of the event. In this case, we are looking for the probability of not getting 4. Since there are six possible outcomes, we need to count the favorable outcomes (not getting 4) and divide it by the total number of outcomes.

The numbers that are not 4 are 1, 2, 3, 5, 6. There are five favorable outcomes, so the probability is 5/6. Therefore, option 5/6 is the correct answer.

4. Odds in favor of guessing the right answer: This question is asking for the odds in favor of guessing correctly. The odds can be expressed as a ratio of the number of favorable outcomes to the number of unfavorable outcomes.

Since there are five possible answers with only one correct answer, there is one favorable outcome and four unfavorable outcomes. The odds in favor of guessing correctly are 1:4. Therefore, option 1:4 is the correct answer.

So, to summarize:
1. P(number < 2) = 1/6
2. P(number ≥ 3) = 5/6
3. P(complement of 4) = 5/6
4. Odds in favor of guessing the right answer = 1:4