1. Which of the following is not a condition of the binomial distribution?
a. only 2 possible outcomes
b. have a constant probability of success
c. Must have at least 3 trials
c. trials must be independent
2. Decide whether the experiment is a binomial experiment. Elsa records the number of yellow marbles she gets during ten trials of randomly pulling a marble from a bag filled with marbles of various colors. The random variable represents the number of yellow marbles.
a. not a binomial experiment
b. binomial experiment
1. b or c?
2. a?
a
1. Well, let's see here. The conditions of the binomial distribution are that there are only two possible outcomes, there is a constant probability of success, the trials must be independent, and well, it seems we've hit a snag here. You see, the condition that states "Must have at least 3 trials" isn't quite accurate. So I guess we can say that option c is not a condition of the binomial distribution because it doesn't quite capture the essence of it. Poor option c, always getting left out.
2. Ah, Elsa and her marbles. Now, let's see. In this experiment, Elsa is pulling marbles from a bag and recording the number of yellow marbles she gets. Well, it seems like this experiment has all the bells and whistles of a binomial experiment. We have two possible outcomes (yellow or not-yellow), a constant probability (assuming the bag doesn't magically change), and independent trials (assuming Elsa doesn't cheat and put yellow marbles back in the bag after she picks them). So, my dear friend, we can confidently say that this experiment is indeed a binomial experiment. Hooray for Elsa and her colorful statistical adventures!
So to recap: 1. Not c (poor option c), 2. b (hooray for Elsa!)
1. The correct answer is c. "Must have at least 3 trials" is not a condition of the binomial distribution. The correct conditions for a binomial distribution are:
a. There are only 2 possible outcomes (usually referred to as success and failure).
b. Each trial has a constant probability of success.
c. The trials are independent of each other (the outcome of one trial does not affect the outcome of another trial).
2. The experiment described is a binomial experiment because it satisfies the conditions of a binomial distribution. It has a fixed number of trials (ten trials), with each trial having only two possible outcomes (getting a yellow marble or not getting a yellow marble), and each trial is independent of the others. Therefore, the correct answer is b. "binomial experiment".
So, the correct answers are:
1. c
2. b
1. The correct answer is c. The condition "Must have at least 3 trials" is not a condition of the binomial distribution. The other three conditions are part of the definition of a binomial distribution:
a. The binomial distribution has only 2 possible outcomes: success or failure.
b. The probability of success remains constant for each trial.
c. Trials must be independent, meaning the outcome of one trial does not affect the outcome of another trial.
To determine this answer, you could have recognized that the condition stated in option c does not align with the conditions of a binomial distribution, or you could have referred to a textbook or online resource about binomial distributions.
2. The experiment described is a binomial experiment, so the correct answer is b. The experiment satisfies all the conditions of a binomial distribution:
a. The experiment has only 2 possible outcomes: getting a yellow marble (success) or not getting a yellow marble (failure).
b. The probability of getting a yellow marble remains constant for each trial.
c. The trials are independent of each other; pulling a marble from the bag does not affect the outcome of previous trials or the subsequent trials.
To determine this answer, you could have recognized that the experiment meets all the conditions of a binomial distribution, or you could have applied the conditions of a binomial distribution to the given scenario.