A piece of equipment will function only when the three components A, B and C are working. The probability of A failing during one year is 0.15, that of B failing is 0.05, and that of C failing is 0.10. What is the probability that the equipment will fail before the end of the
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A piece of equipment will
are working. The
0.05, and that of C failing is 0.10. What is the probability that the equipment will
fail before the end of the year?
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- The probability of an investor investing his savings in foreign currency is 0.45, the probability of investing in gold is 0.42, and the probability of buying government bonds is 0.37. In addition, the probability of the investor to invest his savings in foreign currency and gold is 0.10, the probability of buying both foreign currency and government bonds is 0.12, the probability of buying both gold and government bonds is 0.20, and the probability of buying all three is 0.05. Which of the following is the probability that this investor will use at least one of these three investment tools?The big day came and Kyle is too nervous about whether he passed the exam or not. Kyle has 3 courses taken, course A, course B, and course C., in his exam and each is delivered per envelope. The probability that Kyle passed each of the courses is 55% with a passing grade being 50. Max answered more on course A with 50%. Max answered on course B with 20%. Max answered least on course C with 10%. a. Did Max pass the exam? Prove your answer. b. Construct a tree diagram.A class contains 50 students. The probability of failing in one of the courses for each student is 0.035, but there is no chance to fail in more than one course. You know that a student failed in a course, the probability that the fail reason in non-attendance is 0.025. All other fail reasons are low average. The examinations are private, so the results are mutually independent. Let X and Y be the numbers of failed students due to non-attendance and due to low average, respectively, in that class this semester. Find the joint MGF
- Gabrielle has purchased the 2-year extended warranty from a retailer to cover the value of hers new cellphone in case if it gets damaged or becomes inoperable for the price of $25. Gabrielle's cellphone is worth $1400 and the probability that it gets damaged or becomes inoperable during the length of the extended warranty is estimated to be 4%. Let XX be the retailer's profit from selling the extended warranty. Answer the following questions: 1. Create the probability distribution table for XX : XX outcome profit xx ,$ P(X=x)P(X=x) the cellphone gets damaged or becomes inoperable no claim filed 2. Use the probability distribution table to find the following: E[X]=μX=E[X]=μX= dollars. (Round the answer to 1 decimal place.) SD[X]=σX=SD[X]=σX= dollars. (Round the answer to 1 decimal place.)A fire alarm in a school has two independent circuits. The alarm will function if one or both of the circuits are working. If the probability that the first circuit is working is 0.91, and the probability that the second circuit is working is 0.90, what is the probability that the fire alarm will function? The probability is 0.82Please help me answer this question
- An examination consists of two papers , Paper 1 and Paper 2 . The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2 . Given that a student has failed in Paper 2 , the probability of failing in Paper 1 is 0.6 . Then the probability of a student failing in both the papers is equal toA store specializing in mountain bikes is to open in one of two malls. If the first mall is selected, the store anticipates a yearly profit of $825,000 if successful and a yearly loss of $275,000 otherwise. The probability of success is 1/2. If the second mall is selected, it is estimated that the yearly profit will be $550,000 if successful; otherwise, the annual loss will be $165,000. The probability of success at the second mall is 3/4. What is the expected profit for both mall 1 and 2? Which mall should be chosen in order to maximize the expected profit?A machine consists of two components: A and B. The machine needs both components to operate. As soon as one component breaks the machine fails. The time until component A breaks is an exponential with rate λA = 0.4 per year. The time until component B breaks is an exponential with rate λB = 0.4 per year. The two components are independent. Compute the probability the machine remains functional for at least another 3 years.
- The final match of world championship soccer is to be played between England and the Netherlands. The star player for the Dutch team, Dennis Nightmare, has been injured. The probability of his being fit enough to play in the final is being estimated at 75%. Pre-game predictions have estimated that, without Nightmare, the probability of a Dutch win is 30% and with Nightmare, 50%. Later, you hear that the Dutch team has won the match. Without having any other information about the events that occurred, what would you say was the probability that Dennis Nightmare played in the final?Lindo is deciding which course she wants to take in her next college semester. The probability that she enrols in the statistics course is 0.30 and the probability that she enrols in an econometrics course is 0.70. The probability that she will enrol in statistics course Given that she enrols in econometrics course is 0.40. 1. What is the probability that she will enrol in both Stats course AND econometrics course? ANSWER3.12 Mark is deciding which route to take to work. His choices are I = the Interstate and F = Fifth Street.• P(I) = 0.44 and P(F) = 0.55• P(I AND F) = 0 because Mark will take only one route to work.What is the probability of P(I OR F)?
