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
URGENT<br> Which of the following statements is true? Select all that apply.
valina [46]

Answer:

C is true also

Step-by-step explanation:

3 0
3 years ago
What is the lowest prime number 2,3,4,5 please help
just olya [345]

Answer:

the answer is 2 hope this helps :>

3 0
2 years ago
Find the sum for the polynomials
Nana76 [90]
I don’t think you can get a hold of me and
4 0
2 years ago
5.146 rounded to the nearest tenth
Gnom [1K]

Answer:

5.1

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Trials in an experiment with a polygraph include 97 results that include 23 cases of wrong results and 74 cases of correct resul
o-na [289]

Answer:

H0:p= 0.80                 H1: p< 0.80  one tailed test

Step-by-step explanation:

We state the null and alternative hypotheses as that the results are 80 % against the claim that the results are less than 80%.

H0:p= 0.80                 H1: p< 0.80  one tailed test

p2= 0.8 , p1= 74/97= 0.763

q1= 1-0.763= 0.237    q2= 0.2

The level of significance is 0.05 .

The Z∝= ±1.645 for ∝= 0.05

The test statistic used here is

Z= p1-p2/ √pq/n

Putting the values:

Z= 0.763 -0.8 / √ 0.8*0.2/97

z= -0.037/ 0.0406

z= -0.9113

The Z∝ = ±1.645 for ∝= 0.05 for one tailed test.

As the calculated value  does not fall in the critical region  we fail to reject the null hypothesis. There is not sufficient evidence to support  the claim that such polygraph results are correct less than 80% of the time.

Using the normal probability table.

P (Z <  -0.9113)= 1- P(z= 0.9311) = 1- 0.8238= 0.1762

If P- value is smaller than the significance level reject H0.

0.1762> 0.005  Fail to reject H0.

8 0
3 years ago
Other questions:
  • Connie has $660,000 she wants to save. If the FDIC insurance limit per
    11·2 answers
  • Order these numbers from least to greatest-
    9·2 answers
  • 4x-5(x-2)=12x+4-x<br> ??????????????
    8·1 answer
  • I NEED HELP WITHIN AN HOUR!!! HELP!!
    15·2 answers
  • The perimeter of a triangle is 240. Its sides are proportional to 3:4:5. The largest side of the triangle is
    8·1 answer
  • A student mixed 125 grams of sugar, 250 grams of water, and 5 grams of flavoring. The solution weighs?
    9·2 answers
  • Mr. Rubio is buying a burger meal for each member of his family. He buys each family member a burger for $2.75, a drink for $1.3
    5·1 answer
  • A baker has 24 sesame bagels and 36 plain bagels to put into boxes each box must have the same number of each type of bagel what
    9·1 answer
  • Help me again ahhhhhh
    12·1 answer
  • Edward hoppers oil painting nighthawks had a length of 60 inches and a width of 30 inches . A print of the original has a length
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!