Question

solve each of the following problems by realizing it as a binomial experiment. a fair six-sided die is rolled four times. what is the probability that an odd number is thrown twice?

1. danthu
1/2*1/2 = 1/4 is the likelihood of receiving two odd numbers.

### What are the purposes of binomial experiments ?

When an experiment has just two possible results, binomial probability can be used to calculate the likelihood of each outcome (success and failure).
In a binomial circumstance, there are only two outcomes that can occur on each try. Depending on what you want, you may declare one of the possibilities a failure and the other a success. Anything less than a 6 is a failure, whereas a 6 is a triumph.
A binomial experiment is a statistical test that has the following features: The experiment consists of n repeated repetitions. Each experiment has only two possible outcomes. One of these outcomes is known as a success, while the other is known as a failure.
According to the given information
The probability of receiving an odd number on a die is 3/6 = 1/2 and the likelihood of getting two odd numbers is 1/2*1/2 = 1/4 under the usual assumptions (unbiased die, faces numbered 1-6). There are three odd numbers per die (1, 3 and 5).
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2. Calantha
The probability of getting two odd numbers is 1/2*1/2 = 1/4.

### What are binomial experiments used for?

• When there are only two possible outcomes for an experiment, binomial probability may be used to estimate the likelihood of each result (success and failure).
• There are just two outcomes that can happen on each try in a binomial situation. You may label one of the alternatives Fail and the other Succes, depending on what you desire. A 6 on a dice is a success, whereas anything other than a 6 is a failure.
• A statistical experiment with the following characteristics is called a binomial experiment: There are n repeated trials in the experiment. There are only two potential results for each experiment. One of these results is referred to be a success, and the other as a failure.
Making the standard assumptions (unbiased die, faces numbered 1-6), there are three odd numbers per die (1, 3 and 5), so the probability of getting an odd number on a die is 3/6 = 1/2, and the probability of getting two odd numbers is 1/2*1/2 = 1/4.