Find a the shortest distance from d to b

A certain company sends 40% of its overnight mail parcels by means of express mail service A1. Of these parcels, 4% arrive after

Harrizon [31]

Answer:

(a) The probability that a randomly selected parcel arrived late is 0.026.

(b) The probability that a parcel was late was being shipped through the overnight mail service A₁ is 0.615.

(c) The probability that a parcel was late was being shipped through the overnight mail service A₂ is 0.192.

(d) The probability that a parcel was late was being shipped through the overnight mail service A₃ is 0.192.

Step-by-step explanation:

Consider the tree diagram below.

(a)

The law of total probability sates that: $P(A)=P(A|B)P(B)+P(A|B')P(B')$

Use the law of total probability to determine the probability of a parcel being late.

$P(L)=P(L|A_{1})P(A_{1})+P(L|A_{2})P(A_{2})+P(L|A_{3})P(A_{3})\\=(0.04\times0.40)+(0.01\times0.50)+(0.05\times0.10)\\=0.026$

Thus, the probability that a randomly selected parcel arrived late is 0.026.

(b)

The conditional probability of an event A provided that another event B has already occurred is:

$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$

Compute the probability that a parcel was late was being shipped through the overnight mail service A₁ as follows:

$P(A_{1}|L)=\frac{P(L|A_{1})P(A_{1})}{P(L)} \\=\frac{0.04\times 0.40}{0.026} \\=0.615$

Thus, the probability that a parcel was late was being shipped through the overnight mail service A₁ is 0.615.

(c)

Compute the probability that a parcel was late was being shipped through the overnight mail service A₂ as follows:

$P(A_{2}|L)=\frac{P(L|A_{2})P(A_{2})}{P(L)} \\=\frac{0.01\times 0.50}{0.026} \\=0.192$

Thus, the probability that a parcel was late was being shipped through the overnight mail service A₂ is 0.192.

(d)

Compute the probability that a parcel was late was being shipped through the overnight mail service A₂ as follows:

$P(A_{3}|L)=\frac{P(L|A_{3})P(A_{3})}{P(L)} \\=\frac{0.05\times 0.10}{0.026} \\=0.192$

Thus, the probability that a parcel was late was being shipped through the overnight mail service A₃ is 0.192.

4 0

3 years ago

How would you graph, y=-x-2

Natali5045456 [20]

Well you would start at Y= 0(-x) -2. So (0, -2) then you would move to the left by 1 and move down by 1.

6 0

3 years ago

Three randomly selected households are surveyed. /The numbers of people in the households are 1, 3, and 8. Assume that samples o

inn [45]

The question is asking to find the variance for the said samples in the problem ans use the sample data to determine each variance, and base on my further computation and further calculation, I would say that the answer would be the following:
#1. 3.3 -> 1 and 3 -> 2/9
#2. 1-> 0->3/9
#3. 6.3 - > 8 and 3-> 2/9
#4 49-> 1 and 8-> 2/9

8 0

3 years ago

Your brother lends you $125 at an annual interest rate of 25%. If you want to pay no more than $62.50 in simple interest, in how

iren2701 [21]

3. You purchase a car using a $20,000 loan with a 5% simple interest rate. (a) How much interest do you pay on your loan if you pay off the loan in 4 years? Show your work. (b) How much interest do you pay on your loan if you pay off the loan in 2 years? Show your work. (c) How much interest do you save by paying the loan off in 2 years instead of 4? Show your work. Answer:

7 0

3 years ago

Please Help!!!!!!! Emergency

Stolb23 [73]

Answer:

C

15 + x

Step by step explanation

For Company X, the initial cost is 30 cents plus 5 cents per minute, so the expression would be 30 + 5x (x would represent minutes.

For Company Y, the initial cost is 15 cents plus 4 cents per minute, so the expression would be 15 + 4x (x would represent minutes.)

Then subtract the expression of Y from the expression of X to show the difference in value between Y and X.

So, 30 + 5x - (15 +4x)

Distribute the subtraction sign.

30 + 5x - 15 - 4x

Solve across.

15 + x

6 0

3 years ago