100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Solutions for Biomolecular Thermodynamics, 1st Edition Barrick (All Chapters included) $29.49   Add to cart

Exam (elaborations)

Solutions for Biomolecular Thermodynamics, 1st Edition Barrick (All Chapters included)

 6 views  0 purchase
  • Course
  • Biotech
  • Institution
  • Biotech

Complete Solutions Manual for Biomolecular Thermodynamics, 1st Edition by Douglas Barrick ; ISBN13: 9781315380193. (Full Chapters included Chapter 1 to 14).... Chapter 1: Probabilities and Statistics in Chemical and Biothermodynamics. Chapter 2: Mathematical Tools in Thermodynamics. Chapter 3: T...

[Show more]

Preview 3 out of 85  pages

  • December 23, 2023
  • 85
  • 2023/2024
  • Exam (elaborations)
  • Questions & answers
  • Biotech
  • Biotech
avatar-seller
mizhouubcca
Biomolecular Thermodynamics
1st Edition by Douglas Barrick



Complete Chapter Solutions Manual
are included (Ch 1 to 14)




** Immediate Download
** Swift Response
** All Chapters included

, Solution Manual


CHAPTER 1
1.1 Using the same Venn diagram for illustration, we want the probability of
outcomes from the two events that lead to the cross-hatched area shown
below:




A1 A1 ∩ B2 B2


This represents getting A in event 1 and not B in event 2, plus not getting A
in event 1 but getting B in event 2 (these two are the common “or but not
both” combination calculated in Problem 1.2) plus getting A in event 1 and B in
event 2.

1.2 First the formula will be derived using equations, and then Venn diagrams
will be compared with the steps in the equation. In terms of formulas and
probabilities, there are two ways that the desired pair of outcomes can come
about. One way is that we could get A on the first event and not B on the
second ( A1 ∩ (∼ B2 )). The probability of this is taken as the simple product, since
events 1 and 2 are independent:

pA1 ∩ ( ∼B2 ) = pA × p∼B
= pA × (1− pB ) (A.1.1)
= pA − pA pB


The second way is that we could not get A on the first event and we could get
B on the second ((∼A1 ) ∩ B2 ) , with probability

p( ∼ A1 ) ∩ B2 = p∼ A × pB
= (1− pA ) × pB (A.1.2)
= pB − pA pB




K10030_Solution Manual.indd 1 10-07-201

, 2 Solution Manual


Since either one will work, we want the or combination. Because the two ways
are mutually exclusive (having both would mean both A and ∼A in the first
outcome, and with equal impossibility, both B and ∼B), this or combination is
equal to the union { A1 ∩ (∼ B2 )} ∪ {(∼ A1 ) ∩ B2 }, and its probability is simply the sum
of the probability of the two separate ways above (Equations A.1.1 and A.1.2):

p{ A1 ∩ (∼B2 )} ∪ {(~ A1) ∩ B2 } = pA1 ∩ (∼B2 ) + p(∼ A1) ∩ B2
= pA − pA pB + pB − pA pB
= pA + pB − 2 pA pB

The connection to Venn diagrams is shown below. In this exercise we will work
backward from the combination of outcomes we seek to the individual outcomes.
The probability we are after is for the cross-hatched area below.
{ A1 ∩ (∼ B2 )} ∪ {(∼ A1 ) ∩ B2 }




A1 B2


As indicated, the circles correspond to getting the outcome A in event 1 (left)
and outcome B in event 2. Even though the events are identical, the Venn
diagram is constructed so that there is some overlap between these two (which
we don’t want to include in our “or but not both” combination. As described
above, the two cross-hatched areas above don’t overlap, thus the probability of
their union is the simple sum of the two separate areas given below.

A1 ∩ ~B2
~ A1 ∩ B2

pA × p~B
p~A × pB
= pA (1 – pB)
= (1 – pA)pB

A1 ∩ ~B2 ~ A1 ∩ B2



Adding these two probabilities gives the full “or but not both” expression
above. The only thing remaining is to show that the probability of each of
the crescents is equal to the product of the probabilities as shown in the top
diagram. This will only be done for one of the two crescents, since the other
follows in an exactly analogous way. Focusing on the gray crescent above, it
represents the A outcomes of event 1 and not the B outcomes in event 2. Each
of these outcomes is shown below:

Event 1 Event 2


A1 ~B

p~B = 1 – pB
pA



A1 ~B2




K10030_Solution Manual.indd 2 10-07-201

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller mizhouubcca. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $29.49. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

67096 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$29.49
  • (0)
  Add to cart