Before being allowed to enter a maximum-security area at a military installation, a person must pass three independent identification tests: a voice-pattern test, a fingerprint test, and a handwriting test. If the reliability of the first test is 95%, that of the second test is 98.4%, and that of the third is 98.4%, what is the probability that this security system will allow an improperly identified person to enter the maximum-security area? (Round your answer to seven decimal places.)

A bank recently discovered that approximately 1.6% of all commercial loans issued by the bank become delinquent. Norah, the bank's vice president of operations, is stunned by this discovery. In order to be prepared for the next board meeting, she investigates the matter by randomly selecting 554 commercial loans from the bank’s database and reviewing each loan. What is the probability that at least 12 of the loans in the sample are delinquent? Use Excel to find the probability. Round your answer to four decimal places.

Visitors to your website are asked to answer a single “yes or no” survey question before they get access to the content on the page. Among all of the visitors to this page, there are two categories: Random Clicker (RC) and Truthful Clicker (TC). There are two possible answers to the survey: yes and no. Random clickers would click either one with equal probability. You are also given the information that the overall fraction of random clickers is 0.3. After a trial period, you get the following survey results: 65% said Yes and 35% said No. What is your estimate for P(yes | TC), the probability that someone answers “yes” to the survey question, given that they were a truthful clicker? Hint: use the rule of total probability

Name the method of estimating probabilities based on experience or institution.

Exploration studies are conducted in 13 different locations seeking oil fields in Oman. From a retrospective study it has been found that the possibility of a location to truly have an oil field is 25%. This low probability is due to the complexity of the geological conditions and their challenges in Oman. As a result, the chance to invest in exploration and getting no oil fields is 75%. Determine the probability that 4 locations will truly have oil fields? Select one a. o.06 b.0.21 C0.25 d.0.79

Words that are more likely to be contained in a phishing scam are called flagged words. Typically, there is a 94% chance that a phishing scam contains flagged words. There is a 20% chance that regular email contains flagged words. A security company estimates that 4.9% of emails are phishing scams. An email just came through that contains a flagged word. What are the chances that it is a phishing scam? (Enter the probability as a decimal rounded to four decimal places.)

An assembly line produces a tool. The parts are independently sampled one at a time and tested for compliance. Historically, 0.15 of the parts have been found to be non-compliant. What is the probability that the 6th sampled part will be the 3rd part found to be non-compliant?

In 2014, the percentage of the U.S. population that speak English only in the home is 78.9%. Choose 15 U.S. people at random. What is the probability that exactly one-third of them speak English only? At least one-third? What is the probability that at least 9 do not speak English in the home?