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.
B,C i think
The correct answers are:
When a six-sided number cube is rolled three times, X is the number of 2s rolled.
When a six-sided number cube is rolled twice, X is the number of odd numbers rolled.
The variable X has a binomial distribution in the following cases:
1) When a 6-sided number cube is rolled 3 times, and X is the number of 2s rolled.
2) When a 6-sided number cube is rolled twice, and X is the number of odd numbers rolled.
Therefore, the correct options are:
- 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 twice, X is the number of odd numbers rolled.
To determine which distributions have a binomial distribution for the variable X, we need to check if the experiment satisfies the criteria for a binomial distribution.
A random variable X follows a binomial distribution if the following conditions are met:
1. The experiment consists of a fixed number of trials.
2. Each trial has only two outcomes, usually called "success" and "failure."
3. The probability of success (p) remains constant from trial to trial.
4. The trials are independent.
Let's analyze each of the given scenarios.
1. When a 6-sided number cube is rolled 3 times, X is the number of 2s rolled.
- This scenario satisfies the conditions for a binomial distribution. Each roll can be considered a trial, and the outcome of each trial is either getting a 2 (success) or not getting a 2 (failure). The probability of success (p) remains constant, which is 1/6 for a 6-sided number cube. The trials are also independent. Therefore, this scenario is an example of a binomial distribution for X.
2. When a 6-sided number cube is rolled, X is the number of times rolled before a 2 appears.
- This scenario does not satisfy the conditions for a binomial distribution. The number of trials is not fixed here since the number of times rolled before a 2 appears can vary. Therefore, this is not an example of a binomial distribution for X.
3. When a 6-sided number cube is rolled twice, X is the number of odd numbers rolled.
- This scenario does not satisfy the conditions for a binomial distribution. The number of trials is fixed (two rolls), and each roll has two outcomes (odd or even). However, the probability of success (p) is not constant because the probability of rolling an odd number is not the same as the probability of rolling an even number. Therefore, this is not an example of a binomial distribution for X.
4. When a 6-sided number cube is rolled twice, X is the sum of the numbers rolled.
- This scenario does not satisfy the conditions for a binomial distribution. The number of trials is fixed (two rolls), but the outcome of each trial is a sum of two numbers, not a success/failure outcome. Therefore, this is not an example of a binomial distribution for X.
Based on the analysis above, the only scenario that has a binomial distribution for the variable X is:
- When a 6-sided number cube is rolled 3 times, X is the number of 2s rolled.