1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
cricket20 [7]
3 years ago
12

The prior probabilities for events A1 and A2 are P(A1) = 0.30 and P(A2) = 0.55. It is also known that P(A1 ∩ A2) = 0. Suppose P(

B | A1) = 0.20 and P(B | A2) = 0.05. If needed, round your answers to three decimal digits.a) Are A1 and A2 mutually exclusive? b) Compute P(A1 ∩ B) and P(A2 ∩ B). c) Compute P(B). d) Apply Bayes’ theorem to compute P(A1 | B) and P(A2 | B).
Mathematics
1 answer:
k0ka [10]3 years ago
3 0

We're given the following probabilities:

P(A_1)=0.30

P(A_2)=0.55

P(A_1\cap A_2)=0

P(B\mid A_1)=0.20

P(B\mid A_2)=0.05

(a) Yes, A_1 and A_2 are mutually exclusive. This is exactly what zero probability of their intersection means. The two events cannot occur simultaneously.

(b) Use the definition of conditional probability to expand:

P(A_1\cap B)=P(A_1)P(B\mid A_1)=0.30\cdot0.20=0.06

P(A_2\cap B)=P(A_2)P(B\mid A_2)=0.55\cdot0.05=0.0275

(c) By the law of total probability,

P(B)=P(A_1\cap B)+P(A_2\cap B)=0.06+0.0275=0.0875

(d) Bayes' theorem says

P(A_1\mid B)=\dfrac{P(A_1)P(B\mid A_1)}{P(B)}=\dfrac{0.30\cdot0.20}{0.0875}\approx0.686

P(A_2\mid B)=\dfrac{P(A_2)P(B\mid A_2)}{P(B)}=\dfrac{0.55\cdot0.05}{0.0875}\approx0.314

You might be interested in
Brian can lay a slab of concrete in 6 hours, while Greg can do it in 4 hours. If Brian and Greg work together, how long will it
anastassius [24]

Answer:

2 2/5 hours

Step-by-step explanation:

In 6 hours Brian can lay 1 slab of concrete

dividing both side by 6

in 6/6 hours Brian can lay 1/6 slab of concrete

Thus, in 1 hour  Brian can lay 1/6 slab of concrete

In 4 hours Greg can lay 1 slab of concrete

dividing both side by 4

in 4/4 hours Greg can lay 1/4 slab of concrete

Thus, in 1 hour  Greg can lay 1/4 slab of concrete

Thus, total part of slab laid by both in 1 hour when they work together

1/6 + 1/4 = 4+6/(6*4) = 10/24 = 5/12

5/12 of slab of concrete is laid by both of them in 1 hour

time taken to lay 5/12 of slab = 1 hour

dividing both side by 5/12

time taken to  5/12/ 5/12 of slab = 1/5/12 hour = 12/5 hours

time taken to 1/1 of slab = 12/5 hours = 2 2/5 hours

Thus,

it takes 2 2/5 hours to lay the full slab of concrete when Brian and Greg work together,

5 0
3 years ago
A closet contains 8 shirts, 5 skirts, and 6 pairs of shoes. How many possible outfit combinations are there?
german
since an outfit depends on the on the type of clothes worn @ time
  
8 shirts × 5 skirts × 6 pairs 
         = 240

Answer = 240 0utfit combination
8 0
3 years ago
Read 2 more answers
Marco has a bag of 50 colored marbles.there are 12 blue marbles,18 black marbles,and 20 red marbles.what is the ratio of the num
iren2701 [21]

The answer is 2:3 because it is 12:18 simplified.

8 0
2 years ago
1. Simplify. 4(2a - 1) - 4 + 7a ​
daser333 [38]

Answer:

<em><u>=15a−8</u></em>

Step-by-step explanation:

Let's simplify step-by-step.

4(2a−1)−4+7a

Distribute:

=(4)(2a)+(4)(−1)+−4+7a

=8a+−4+−4+7a

Combine Like Terms:

=8a+−4+−4+7a

=(8a+7a)+(−4+−4)

=15a+−8

Answer:

=15a−8

hope i helped

-lvr

4 0
3 years ago
What is the value of X?
Paul [167]

Answer:

x = 41 ft

Step-by-step explanation:

35(35+23) = 29(29+x)

2030 = 29(29+x)

70 = 29 + x

x = 41 ft

6 0
3 years ago
Other questions:
  • Best Deal 2
    11·1 answer
  • Write the ratio 2/3 to 8 as a fraction in simplest form
    12·1 answer
  • What percent of 100 is 79?
    11·2 answers
  • A phone company charges a monthly rate of $12.95 and $0.25 a minute per call.
    14·1 answer
  • What is the length of x of the side of the triangle below?
    13·1 answer
  • Solve for an angle in right triangles
    6·1 answer
  • Which describes the
    14·2 answers
  • The number of adults at an amusement park, measured in hundreds of people, is represented by the function a(w)=−0.4w^2+5w+9, whe
    9·1 answer
  • Please help me 1. Find the missing angle.
    6·1 answer
  • Find the value of x. x°+65°+109°+136°=310°
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!