100% de satisfacción garantizada Inmediatamente disponible después del pago Tanto en línea como en PDF No estas atado a nada
Buscado previamente por ti
Solutions Manual for Biomolecular Thermodynamics, From Theory to Application, 1st Edition by Douglas Barrick (All Chapters) A+ 12,78 €
Añadir al carrito
Biomolecular Thermodynamics, From Theory to Applic
Todos documentos para esta materia (1)
Vendedor
Seguir
ASolution
Comentarios recibidos
Vista previa del contenido
Created By: A Solution
Solutions Manual for Biomolecular Thermodynamics, From Theory
to Application, 1st Edition by Douglas Barrick (All Chapters) A+
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:
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:
1
,Created By: A Solution
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):
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.
2
,Created By: A Solution
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.
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:
3
, Created By: A Solution
Because Event 1 and Event 2 are independent, the “and” combination of these two outcomes is
given by the intersection, and the probability of the
intersection is given by the product of the two separate probabilities, leading to the expressions
for probabilities for the gray cross-hatched crescent.
(a) These are two independent elementary events each with an outcome probability of 0.5.
We are asked for the probability of the sequence H1 T2, which requires multiplication of the
elementary probabilities:
We can arrange this probability, along with the probability for the other three possible sequences,
in a table:
Toss 1
Toss 2 H (0.5) T (0.5)
H (0.5) H1H2 T1H2
(0.25) (0.25)
T (0.5) H1T2 T1T2
(0.25) (0.25)
The probability of getting a head on the first toss or a tail on the second toss, but not both, is
4
Los beneficios de comprar resúmenes en Stuvia estan en línea:
Garantiza la calidad de los comentarios
Compradores de Stuvia evaluaron más de 700.000 resúmenes. Así estas seguro que compras los mejores documentos!
Compra fácil y rápido
Puedes pagar rápidamente y en una vez con iDeal, tarjeta de crédito o con tu crédito de Stuvia. Sin tener que hacerte miembro.
Enfócate en lo más importante
Tus compañeros escriben los resúmenes. Por eso tienes la seguridad que tienes un resumen actual y confiable.
Así llegas a la conclusión rapidamente!
Preguntas frecuentes
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.
100% de satisfacción garantizada: ¿Cómo funciona?
Nuestra garantía de satisfacción le asegura que siempre encontrará un documento de estudio a tu medida. Tu rellenas un formulario y nuestro equipo de atención al cliente se encarga del resto.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller ASolution. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for 12,78 €. You're not tied to anything after your purchase.
