Q1) Two drugs that relieve pain are available to treat patients. Drug A has been found to be effective in three quarters of all patients; when it is effective, the patients have relief from pain one hour after taking this drug. Drug B acts quicker but only works with one half of all patients: those who benefit from this drug have relief of pain after 30 mins. The physician cannot decide which patients should be prescribed which drug so he prescribes randomly. Assuming that there is no variation between patients in the times taken to act for either drug. calculate the probability that: (a) a patient is prescribed drug B and is relieved of pain; (b) a patient is relieved of pain after one hour; (c) a patient who was relieved of pain after one hour took drug A: (d) two patients receiving different drugs are both relieved of pain after one hour. (e) out of six patients treated with the same drug. three are relieved of pain after one hour and three are not.

Essentials of Business Analytics (MindTap Course List)
2nd Edition
ISBN:9781305627734
Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson
Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson
Chapter2: Descriptive Statistics
Section: Chapter Questions
Problem 21P: Return to the waiting times given for the physicians office in Problem 19. a. Considering only...
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Q1) Two drugs that relieve pain are available to treat patients. Drug A has been found to be
effective in three quarters of all patients; when it is effective, the patients have relief from pain
one hour after taking this drug. Drug B acts quicker but only works with one half of all patients:
those who benefit from this drug have relief of pain after 30 mins. The physician cannot decide
which patients should be prescribed which drug so he prescribes randomly.
Assuming that there is no variation between patients in the times taken to act for either drug.
calculate the probability that:
(a) a patient is prescribed drug B and is relieved of pain;
(b) a patient is relieved of pain after one hour;
(c) a patient who was relieved of pain after one hour took drug A;
(d) two patients receiving different drugs are both relieved of pain after one hour.
(e) out of six patients treated with the same drug, three are relieved of pain after one hour and
three are not.
Q2) In the National Lottery you need to choose 6 balls from 49. What is the probability that I
choose all 6 balls correctly?
There are 2 ways of answering this question
) using permutations and combinations
(i) using a tree diagram
Q3) In a certain assembly plant, three machines, B1, B2, and B3, make 30%, 45%, and 25%,
respectively, of the products. It is known from past experience that 2%, 3%, and 2% of the
products made by each machine, respectively. are defective. Now, suppose that a finished
product is randomly selected. What is the probability that it is defective?
Q3) A statistics class for engineers consists of 25 industrial, 10 mechanical, 10 electrical, and 8
civil engineering students. If a person is randomly selected by the instructor to answer a
question, find the probability that the student chosen is
(a) an industrial engineering major and
(b) a civil engineering or an electrical engineering major.
Q4) You collect hockey trading cards. For one team there are 25 different cards in the set, and
you have all of them except for the starting goalie card. To try and get this card, you buy 8
packs of 5 cards each. All cards in a pack are different and each of the cards is équally likely to
be in a given pack. Find the probability that you will get at least one starting goalie card.
Transcribed Image Text:Q1) Two drugs that relieve pain are available to treat patients. Drug A has been found to be effective in three quarters of all patients; when it is effective, the patients have relief from pain one hour after taking this drug. Drug B acts quicker but only works with one half of all patients: those who benefit from this drug have relief of pain after 30 mins. The physician cannot decide which patients should be prescribed which drug so he prescribes randomly. Assuming that there is no variation between patients in the times taken to act for either drug. calculate the probability that: (a) a patient is prescribed drug B and is relieved of pain; (b) a patient is relieved of pain after one hour; (c) a patient who was relieved of pain after one hour took drug A; (d) two patients receiving different drugs are both relieved of pain after one hour. (e) out of six patients treated with the same drug, three are relieved of pain after one hour and three are not. Q2) In the National Lottery you need to choose 6 balls from 49. What is the probability that I choose all 6 balls correctly? There are 2 ways of answering this question ) using permutations and combinations (i) using a tree diagram Q3) In a certain assembly plant, three machines, B1, B2, and B3, make 30%, 45%, and 25%, respectively, of the products. It is known from past experience that 2%, 3%, and 2% of the products made by each machine, respectively. are defective. Now, suppose that a finished product is randomly selected. What is the probability that it is defective? Q3) A statistics class for engineers consists of 25 industrial, 10 mechanical, 10 electrical, and 8 civil engineering students. If a person is randomly selected by the instructor to answer a question, find the probability that the student chosen is (a) an industrial engineering major and (b) a civil engineering or an electrical engineering major. Q4) You collect hockey trading cards. For one team there are 25 different cards in the set, and you have all of them except for the starting goalie card. To try and get this card, you buy 8 packs of 5 cards each. All cards in a pack are different and each of the cards is équally likely to be in a given pack. Find the probability that you will get at least one starting goalie card.
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