In which distributions does the variable, X, have a binomial distribution?

(Choose all that are correct)
~When a 6-sided number cube is rolled 3 times, X is the number of 2s rolled.
~When a 6-sided number cube is rolled, X is the number of times rolled before a 2 appears.
~When a 6-sided number cube is rolled twice, X is the number of odd numbers rolled.
~When a 6-sided number cube is rolled twice, X is the sum of the numbers rolled.

@yibj you can't make me mad

@yibj no u

this is incorrect

To determine if a variable follows a binomial distribution, we need to check if the following conditions are satisfied:

1. The random experiment consists of a fixed number of independent trials.
2. Each trial has only two possible outcomes, labeled as success and failure.
3. The probability of success remains constant for each trial.
4. The trials are independent of each other.

Let's examine each scenario to determine if the variable X follows a binomial distribution:

1. When a 6-sided number cube is rolled 3 times, X is the number of 2s rolled.
In this case, each trial (rolling the number cube) has two possible outcomes (getting a 2 or not getting a 2). The probability of success (rolling a 2) remains constant. The random trials are independent.
Therefore, X follows a binomial distribution in this scenario.

2. When a 6-sided number cube is rolled, X is the number of times rolled before a 2 appears.
In this case, the number of trials is not fixed since the number of rolls until a 2 appears may vary. Thus, it does not satisfy the first condition.
Therefore, X does not follow a binomial distribution in this scenario.

3. When a 6-sided number cube is rolled twice, X is the number of odd numbers rolled.
In this case, each trial (rolling the number cube) has two possible outcomes (getting an odd number or not getting an odd number). The probability of success (getting an odd number) remains constant. The random trials are independent.
Therefore, X follows a binomial distribution in this scenario.

4. When a 6-sided number cube is rolled twice, X is the sum of the numbers rolled.
In this case, the variable X represents the sum of two numbers, which can take on multiple values. It does not satisfy the second condition (only two possible outcomes).
Therefore, X does not follow a binomial distribution in this scenario.

Based on our analysis, the variable X has a binomial distribution in the first and third scenarios mentioned above.

hey @yibj

That s so rude @Alex was asking a math question You need to leave this site and dont come back untill you have fixed ur additude