An oil exploration company currently has two active projects, one in Asia and the other in Europe. Let A be the event that the Asian project is successful and B be the event that the European project is successful. Suppose that A and B are independent events with P(A) = 0.9 and P(B) = 0.3. (a) If the Asian project is not successful, what is the probability that the European project is also not successful? Explain your reasoning. O Since the events are not independent, then A' and B'are mutually exclusive. O Since the events are independent, then A' and B' are mutually exclusive. O Since the events are independent, then A' and B' are not independent. O Since the events are independent, then A' and B' are independent. (b) What is the probability that at least one of the two projects will be successful? (c) Given that at least one of the two projects is successful, what is the probability that only the Asian project is successful? (Round your answer to three decimal places.)

An oil exploration company currently has two active projects, one in Asia and the other in Europe. Let A be the event that the Asian project is successful and B be the event that the European project is successful. Suppose that A and B are independent events with P(A) = 0.9 and P(B) = 0.3. (a) If the Asian project is not successful, what is the probability that the European project is also not successful? Explain your reasoning. O Since the events are not independent, then A' and B'are mutually exclusive. O Since the events are independent, then A' and B' are mutually exclusive. O Since the events are independent, then A' and B' are not independent. O Since the events are independent, then A' and B' are independent. (b) What is the probability that at least one of the two projects will be successful? (c) Given that at least one of the two projects is successful, what is the probability that only the Asian project is successful? (Round your answer to three decimal places.)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Joon wants to determine whether his San Jose oil field will yield oil. He has hired a geologist to run tests on the field. If there is oil in the field, there is a 95% chance that the test will indicate oil. If the field contains no oil, there is a 5% chance that the test will indicate oil. If the test indicates that there is no oil in the field, what is the probability that the field contains oil? Before the test, Joon believes that there is a 10% chance that the field will yield oil.
An oil exploration company currently has two active projects, one in Asia and the other in Europe. Let A be the event that the Asian project is successful and B be the event that the European project is successful. Suppose that A and B are independent events with P(A) = 0.3 and P(B) = 0.5. (a) If the Asian project is not successful, what is the probability that the European project is also not successful? Explain your reasoning. O Since the events are independent, then A' and B' are mutually exclusive. O Since the events are independent, then A' and B' are not independent. O since the events are independent, then A' and B' are independent. O Since the events are not independent, then A' and B' are mutually exclusive. (b) What is the probability that at least one of the two projects will be successful? (c) Given that at least one of the two projects is successful, what is the probability that only the Asian project is successful? (Round your answer to three decimal places.)
A couple has two children. Let A be the event that their first child is a boy, and note that P(A)=51.2%. Let B be the event that their second child is a girl, with P(B)=48.8%. A and B are independent events. What is the probability that the couple has a first child that is a boy and a second child that is a girl? Give your answer as a decimal rounded to two decimal places.
Tahir travels by flight from Kuala Lumpur to Istanbul with a connection flight in Abu Dhabi. The probability that his first flight leaves on time is 0.18. If the flight is on time, the probability that his luggage will make the connecting flight in Abu Dhabi is 0.88, but if the first flight is delayed, the probability that the luggage will make it is only 0.58. (i) Are the first flight leaving on time and the luggage making the connection independent events? Explain. (ii) Calculate the probability that his luggage arrives in Istanbul with him. (ii) Suppose that Haneen pick him up at the Istanbul airport, and his luggage is not there. Calculate the probability that Tahir first flight was delayed.
Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you receive an Athletic scholarship is 0.22. The probability of receiving both scholarships is 0.14. The probability of getting at least one of the scholarships is 0.35. (a) What is the probability that you will receive a Merit scholarship? (b) Are Events A and M mutually exclusive? Why or why not? Explain. Yes, because P(A ∩ M) = 0.Yes, because P(A ∩ M) ≠ 0. No, because P(A ∩ M) ≠ 0.No, because P(A ∩ M) = 0. (c) Are Events A and M independent? Explain using probabilities. Yes, because P(A ∩ M) = P(A)P(M).Yes, because P(A ∩ M) ≠ P(A)P(M). No, because P(A ∩ M) = P(A)P(M).No, because P(A ∩ M) ≠ P(A)P(M). (d) What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship? (Round your answer to four decimal places.) (e) What is the probability of receiving the Merit scholarship…
Events A and B are independent events with P(A) = 0.25 and P(B) = 0.35. The probability of the complement of Event B equals
Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows. Answer questions 6-9. Undergraduate Major Business Engineering Other Totals Full-Time 352 197 251 800 Intended Enrollment Part- 150 161 194 505 Status Time Totals 502 358 445 1305
Sick computers: Let V be the event that a computer contains a virus, and let W be the event that a computer contains a worm. Suppose P (V)=0.25, P (W)=0.62, P (V and W)=0.11. (a) Find the probability that the computer contains either a virus or a worm or both. (b) Find the probability that the computer does not contain a worm. Part 1 of 2 (a) Find the probability that the computer contains either a virus or a worm or both. The probability that the computer contains either a virus or a worm or both is Part 2 of 2 (b) Find the probability that the computer does not contain a worm. The probability that the computer does not contain a worm is X X
A couple has two children. Let A be the event that their first child is a boy and note that P(A) = 0.512. Let B be the event that their second child is a girl, with P(B) = 0.488. A and B are independent events. What is the probability that the couple has first child that is a boy and a second child that is a girl?
Suppose you have 3 events A,B,C and exactly one happens and are equally likely. There is another event E and we know P(E|A)=.4, P(E|B)=.7, and P(E|C)=.8. Suppose we don't know if A,B, or C was the event that happened, but we do know E happened. Find the three probabilities that A happened, B happened, and C happened.
Tina Fey goes trick-or-treating the night of Halloween dressed as Sarah Palin. She visits homes in her neighborhood to collect candy, but only receives candy, naturally, when the door is answered and the family still has a piece of candy to give away. Upon knocking, the probability of the door being answered is 3/4, and the probability that the home still has candy is 2/3. Assume that the events “Door answered” and “candy remaining” are independent and also that the outcomes at each home are independent. Also assume that each home gives away at most a single piece of candy. (c) Determine the probability that she receives her second piece of candy at the fifth house. (d) Given that she did not receive her second piece of candy at the second house(not sure if she receive her first candy), determine the conditional probability that she will receive her second piece of candy at the fifth house.