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
Anna71 [15]
3 years ago
13

The prior probabilities for events A1 and A2 are P(A1) = 0.35 and P(A2) = 0.50. 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? Explain your answer. The input in the box below will not be graded, but may be reviewed and considered by your instructor. (b) Compute P(A1 ∩ B) and P(A2 ∩ B). P(A1 ∩ B) = 0.2 P(A2 ∩ B) = 0.05 (c) Compute P(B). P(B) = (d) Apply Bayes’ theorem to compute P(A1 | B) and P(A2 | B). P(A1 | B) = P(A2 | B) =
Mathematics
1 answer:
forsale [732]3 years ago
5 0

Answer:

Step-by-step explanation:

Hello!

Given the probabilities:

P(A₁)= 0.35

P(A₂)= 0.50

P(A₁∩A₂)= 0

P(BIA₁)= 0.20

P(BIA₂)= 0.05

a)

Two events are mutually exclusive when the occurrence of one of them prevents the occurrence of the other in one repetition of the trial, this means that both events cannot occur at the same time and therefore they'll intersection is void (and its probability zero)

Considering that P(A₁∩A₂)= 0, we can assume that both events are mutually exclusive.

b)

Considering that P(BIA)= \frac{P(AnB)}{P(A)} you can clear the intersection from the formula P(AnB)= P(B/A)*P(A) and apply it for the given events:

P(A_1nB)= P(B/A_1) * P(A_1)= 0.20*0.35= 0.07

P(A_2nB)= P(B/A_2)*P(A_2)= 0.05*0.50= 0.025

c)

The probability of "B" is marginal, to calculate it you have to add all intersections where it occurs:

P(B)= (A₁∩B) + P(A₂∩B)=  0.07 + 0.025= 0.095

d)

The Bayes' theorem states that:

P(Ai/B)= \frac{P(B/Ai)*P(A)}{P(B)}

Then:

P(A_1/B)= \frac{P(B/A_1)*P(A_1)}{P(B)}= \frac{0.20*0.35}{0.095}= 0.737 = 0.74

P(A_2/B)= \frac{P(B/A_2)*P(A_2)}{P(B)} = \frac{0.05*0.50}{0.095} = 0.26

I hope it helps!

You might be interested in
Someone help me please? giving away 35 points and brainliest (only if right)
lisabon 2012 [21]
Triangle from angles XBR=130 cm
Triangle from angles YNJ=65cm
8 0
3 years ago
Need help with angle solving​
laiz [17]

Step-by-step explanation:

corresponding angles (CA)

Alternative interior angles (AIA)

co interior angles (CIA)

  1. question 1 angles =

5 + 3 = 180 ( CIA)

83⁰ + 3 = 180

angle 3 = 180 - 83⁰

angle 3 = 97

angle 8 = angle 3.... CA

angle 8 = angle 16 ....CA

ANGLE 16 = ANGLE 12.....CA

angle 5 = angle 13 ....CA

ANGLE 3 = Angle 6......AIA

ANGLE 5 = ANGLE 4.......AIA

ANGLE 4 = ANGLE 7......CA

ANGLE 6 = ANGLE 1......CA

ANGLE 13 = ANGLE 9......CA

ANGLE 12 = ANGLE 14.....AIA

ANGLE 13 = ANGLE 11.....AIA

ANGLE 14 = ANGLE 10.......CA

ANGLE 11 = ANGLE 15

NOW JUST PUT THE VALUES GIVEN IN QUESTION AND AT THE TOP OF MY ANSWER IN EACH CASE AND UR DONE.....

QUESTION 2 :

ANGLE 1 = ANGLE 7 .......AIA

2X + 40 = 6X - 20

40 + 20 = 6X - 2X

60 = 4X

60/4 = X

15⁰ = X

SO, ANGLE 7 = 6× 15 -20 = 90 - 20 = 70⁰

AND, ANGLE 1 = 2 × 15 + 40 = 30 + 40 = 70⁰

ANGLE 7 = ANGLE 3 ......CA

ANGLE 3 = ANGLE 5 .....AIA

ANGLE 3 + ANGLE 6 = 180 .....CIA

70 + ANGLE 6 = 180⁰

ANGLE 6 = 180 - 70⁰ = 110⁰

angle 2 = Angle 6

ANGLE 2 = ANGLE 8.....AEA ALTERNATIVE EXTERIOR ANGLE

ANGLE 8 = ANGLE 4

NOW, JUST PUT THE VALUES I HAVE WRITTEN ABOVE ACCORDINGLY IN EACH CASE....

Did I really jst got 15 points for this (ノ`Д´)ノ彡

HEHEEE JK:)

8 0
2 years ago
Help me answer dis .
iren [92.7K]

Answer:

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Find the area of the triangle. 5 ft 8 ft ​
natima [27]

Answer:

40

Step-by-step explanation:

The formula for area is LxW, in this case it’s 5x8 which is 40.

8 0
3 years ago
Read 2 more answers
I need help with this
SVETLANKA909090 [29]

Answer:

The answer is 0.675

Step-by-step explanation:

If you were going to ask Brainly, you could have easily just used a calculator lol

4 0
3 years ago
Other questions:
  • If a number is divided by a negative number will the outcome be positive?
    6·1 answer
  • To make a profit, Ethan knows that his prime cost of producing a part must be no more than $189.27. It takes 2 hours for a machi
    5·1 answer
  • What is 2.6% written as a decimal
    8·2 answers
  • I need help plzz I need the answer
    7·1 answer
  • Factory2 + 5y +6.<br>(y + 2MY + 4)<br>(y + 1)x + 5)<br>(y + 2)(y + 3)<br>.............​
    14·1 answer
  • Find the perimeter of triangle ABC
    9·1 answer
  • Can someone please help me fill in the table for f(x) = -1/4(6)^x
    10·1 answer
  • HELP HOW DO I GET MORE THAN ONE PICTURE WHEN I ASK A QUESTION ‍♀️‍♀️
    7·1 answer
  • Sue has 18 3/4 cups of sugar Each pie calls for 1 1/2 cup of sugar Sue wants to break 12 pies Does she have enough sugar How muc
    9·1 answer
  • Plzzz help i will give you a branlest Given this equation;
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!