Transcript The Problem (dine at your own risk)

The Problem
(dine at your own risk)
Of the 150 customers who ate dinner last night at the
Palazzo di Sporcizie 66 had a fish entree, 72 a meat
entree, the rest ate a vegan meal. Historically four in ten
Palazzo’s customers who have a fish entree develop
some stomach trouble within twelve hours of their meal.
For meat eaters the rate is 3 in ten, while only one in ten
vegans develops stomach trouble in that time limit. This
morning at lunch you hear a person saying: “Yesterday I
ate dinner at the Palazzo di Sporcizie , it was excellent, I
had no trouble at all, except for the price.” Is the person
you overheard most likely to be a fish eater, a meat
eater, or a vegan?
The Problem
(Let’s be serious now)
150 Alzheimer’s disease (AD) patients recently
participated in a research study.
Four medications are currently approved by regulatory
agencies such as the U.S. Food and Drug Administration
(FDA) and the European Medicines Agency (EMA) to
treat the cognitive manifestations of AD: three are
acetylcholinesterase inhibitors and the other is
memantine, an NMDA receptor antagonist.
No drug has an indication for delaying or halting the
progression of the disease.
The Problem (Continued)
44% of the AD patients participating in the study received
an acetylcholinesterase inhibitor, 48% were treated with
memantine, the remaining patients, due to their
remarkably good physical conditions, received a
placebo.
Past research suggests that 40% of AD patients on an
acetylcholinesterase inhibitor show remarkable
improvement, the drug memantine improves the
conditions of about 30% of the patients treated with it,
and 10% of AD patients in good physical conditions
show improvement if left untreated.
A patient picked at random from the 150 has shown no
improvement. Which drug (or the placebo) is most likely
to have been used with this patient?
The Solution(s)
The sample space S has
150 sample points
(customers/AD patients)
The Event of Interest is:
• For Dining Customers :
No stomach trouble
• For AD patients :
No improvement
We do the calculations on the
blackboard
We need to compute:
(They must be “givens.”)