The Probability of Success and the Probability of Failure: p and q

The probability of success (symbolized p) is at the heart of the binomial probability distribution. This number is obtained on the basis of prior knowledge or theory. In the present example pertaining to pretrial release, we know that 62% of felony defendants obtain pretrial release. This means that each defendant’s probability of release is p = .62.

We know that release is not the only possible outcome, though—defendants can be detained, too. The opposite of a success is a failure. Because we are dealing with events that have two potential outcomes, we need to know the probability of failure in addition to that of success. The probability of failure is represented by the letter q ; to compute the value of q , the bound rule and the rule of the complement must be invoked. In Chapter 5, you learned that

Don't use plagiarized sources. Get Your Custom Essay on
The Probability of Success and the Probability of Failure: p and q
Just from $13/Page
Order Essay

p (A) + p (Not A) = 1.00; therefore,

p (Not A) = 1.00 – p (A) .

Failure: Any outcome other than success or the event of interest.

What we are doing now is exactly the same thing, with the small change that p (A) is being changed to simply p , and p (Not A) will now be represented by the letter q. So,

With q = .62, the probability that a felony defendant will be detained prior to trial (i.e., will not obtain pretrial release) is

q = 1.00 – .62 = .38

Putting It All Together: Using the Binomial Coefficient to Construct the Binomial Probability Distribution

Using p and q , the probability of various combinations of successes and failures can be computed. When there are r successes over N trials, then there are N – r failures over that same set of trials. There is a formula called the restricted multiplication rule for independent events that guarantees that the probability of r successes and N – r failures is the product of p and q. In the present example, there are three successes (each with probability p = .62) and two failures (each with probability q = .38). You might also recall from prior math classes that exponents can be used as shorthand for multiplication when a particular number is multiplied by itself many times. Finally, we also have to account for the combination of N and r. The probability of three successes is thus

= 10(.24)(.14)

= .34

Academic Heros
Calculate your paper price
Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

Our writers are encouraged to read and research widely to have rich information before writing clients’ papers. Therefore, be it high school or PhD level paper, it will always be a well-researched work handled by experts.

Professional and Experienced Academic Writers

For one to become part of our team, thorough interview and vetting is undertaken to make sure their academic level and experience are beyond reproach, hence enabling us give our clients top quality work.

Free Unlimited Revisions

Once you have received your paper and feel that some issues have been missed, just request for revision and it will be done. In addition, you can present your work to the tutor and he/she asks for improvement/changes, we are always ready to assist.

Prompt Delivery and 100% Money-Back-Guarantee

All our papers are sent to the clients before the deadline to allow them time to review the work before presenting to the tutor. If for some reason we feel our writers cannot meet the deadline, we will contact you to ask for more time. If this is not possible, then the paid amount will be refunded.

Original & Confidential

Our writers have been trained to ensure work produced is free of plagiarism. Software to check originality are also applied. Our clients’ information is highly guarded from third parties to ensure confidentiality is maintained.

24/7 Customer Support

Our support team is available 24 hours, 7 days a week. You can reach the team via live chat, email or phone call. You can always get in touch whenever you need any assistance.

Try it now!

Calculate the price of your order

Total price:

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

You have had a hectic day, and still need to complete your assignment, yet it is late at night. No need to panic. Place your order with us, retire to bed, and once you wake up, the paper will be ready.


Essay Writing Service

It does not matter the urgency of your paper, or the academic level, our team is ready to help you 24/7. Just contact us and all your academic needs will be sorted.


Admission Essays & Business Writing Help

A student is often required to write an admission letter requesting to be admitted in a certain institution. For you to be gain that admission in your dream institution, you must write a convincing letter. You can depend on our team for the best admission letters.


Editing Support

Academic writing is not just about getting information and throwing it all over. Our team will ensure you have a polished paper that is coherent and has a good flow of information. We also ensure the paper follows the correct formatting styles like APA, Harvard, MLA, Chicago/Turabian.


Revision Support

If our writers write a paper but you are not satisfied in one way or another, you can always ask for revision. This is totally free. Our writers and editors will revise your paper untill you are be totally satisfied. We as well offer revision for papers not done by our writers at a small fee.