Suppose that out of 20% of all packages from Amazon are delivered by UPS. 15% of the packages that are delivered by UPS weighs 2 lbs or more. Also, 7% of the packages that are not delivered by UPS weighs less than 2 lbs. a. What is the probability that a package is delivered by UPS if it weighs 2 lbs or more

0.1938 = 19.38% probability that a package is delivered by UPS if it weighs 2 lbs or more

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

In which

P(B|A) is the probability of event B happening, given that A happened.

is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: It weighs 2 lbs or more

Event B: Delivered by UPS

15% of the packages that are delivered by UPS weighs 2 lbs or more.

This means that

More than 2 lbs:

15% of 20%(UPS)

93% of 80%(Not delivered by UPS). So

a. What is the probability that a package is delivered by UPS if it weighs 2 lbs or more

0.1938 = 19.38% probability that a package is delivered by UPS if it weighs 2 lbs or more

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

The answer is in the image 

The answer is in the image 

The solution is given in the image below

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students  

Let the father's age be x and son's be y

10 years before-

Father age=x-10

sons age=y-10

Given,

x-10=10(y-10)

x-10=10y-100

Given present age of father=40

therefore,

x=40

40-10=10y-100

10y-100=30

10y=130

y=130/10

y=13

Therefore present age of son=13years

Volume of rectangular prism=length * width * height

Given,

length=3/8cm

breadth=5/8cm

height=7/8cm

therefore volume=(3/8)*(5/8)*(7/8)

                           =105/512 cm3