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?
To determine the answer for these questions, let's go through the conditions of a binomial distribution:
1. Only 2 possible outcomes: This means that for each trial, there are only two possible outcomes, typically labeled as success and failure. In this case, the outcome is either getting a yellow marble or not getting a yellow marble. Answer: a. only 2 possible outcomes
2. Constant probability of success: The probability of success (getting a yellow marble) remains the same for each trial. This implies that pulling a yellow marble from the bag has the same probability throughout the ten trials. Answer: b. have a constant probability of success
3. At least 3 trials: A binomial distribution requires multiple trials, usually denoted as "n." The number of trials in this experiment is ten trials, which satisfies the condition. Answer: Not applicable
4. Trials must be independent: Each trial is independent of one another, meaning that the outcome of one trial does not affect the outcome of another trial. As long as pulling a marble does not affect the probability or availability of pulling another marble, this condition is satisfied. Answer: c. trials must be independent
Now, let's answer the questions:
1. From the given conditions, the answer is c. Must have at least 3 trials.
2. Elsa's experiment satisfies all the conditions of a binomial experiment, as there are only two possible outcomes (yellow marble or not), the probability of success (getting a yellow marble) remains constant throughout the trials, and the trials are independent. Hence, the answer is b. binomial experiment.