Justify if the following is a binomial.
Rolling a fair die 3 times and observing the number that appears uppermost.
There are 3 trials. So that is fixed. But there doesn't seem to be the two outcomes of success and failure. It isn't really clear in this question.
If it doesn't meet every single rule, then it is not a binomial?
No, earlier problem down below your success was drawing number 6 all three times and failure was any of the other five. That is binary.
If success is drawing the number six three times then your chance is
1/6 * 1/6 * 1/6 = 1/216 , binomial
To determine if the given scenario can be considered a binomial experiment, we need to check for the following characteristics:
1. Fixed number of trials: Yes, the scenario clearly states that the die will be rolled 3 times. Thus, the number of trials is fixed.
2. Independent trials: In this case, rolling a fair die multiple times can be considered independent since the outcome of one roll does not influence the outcome of subsequent rolls. Therefore, this condition is met.
3. Two possible outcomes: For an event to be classified as binomial, there must be two distinct outcomes for each trial, usually referred to as success and failure. However, in the given scenario, rolling a die can result in six possible outcomes (the numbers 1 to 6 appearing on the top face). Therefore, this condition is not met.
Therefore, based on the criteria for a binomial experiment, rolling a fair die 3 times and observing the number that appears uppermost does not qualify as a binomial experiment.