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
Reptile [31]
3 years ago
12

In an experiment, A,B, C, andD are events with probabilitiesP[A UB] = 5/8,P[A] =3/8,

Mathematics
1 answer:
BARSIC [14]3 years ago
7 0

Answer:

Step-by-step explanation:

Hello!

You have 4 events A, B, C and D

With probabilities:

P(A∪B)= 5/8

P(A)= 3/8

P(C∩D)= 1/3

P(C)= 1/2

A and B are disjoint events, this means that there are no shared elements between then and their intersection is void, symbolically A∩B= ∅, in consequence, these events are mutually exclusive.

C and D are independent events, this means that the occurrence of one of them does not affect the probability of occurrence of the other one in two consecutive repetitions.

a.

i. P(A∩B)= 0

⇒ Since A and B are disjoint events, the probability of their intersection is zero.

ii. A and B are mutually exclusive events, this means that P(A∪B)= P(A)+P(B)

⇒ From this expression, you can clear the probability of b as P(B)= P(A∪B)-P(A)= 5/8-3/8= 1/4

iii. If Bc is the complementary event of B, its probability would be P(Bc)= 1 - P(B)= 1 - 1/4= 3/4. If the events A and B are mutually exclusive and disjoint, it is logical to believe that so will be the events A and Bc, so their intersection will also be void:

P(A∩Bc)= 0

vi.P(A∪Bc)= P(A) + P(Bc)= 3/8+3/4= 9/8

b.

If A and B are independent then the probability of A is equal to the probability of A given B, symbolically:

P(A)= P(A/B)

P(A/B)= \frac{P(AnB)}{P(B)}= \frac{0}{1/4}= 0

P(A)= 3/8

P(A) ≠ P(A/B) ⇒ A and B are not independent.

c.

i. P(D) ⇒ Considering C and D are two independent events, then we know that P(C∩D)= P(C)*P(D)

Then you can clear the probability of D as:

P(D)= P(C∩D)/P(C)= (1/3)/(1/2)= 2/3

ii. If Dc is the complementary event of D, then its probability is P(Dc)= 1 - P(D) = 1 - 2/3= 1/3

P(C∩Dc)= P(C)*P(Dc)= (1/2)*(1/3)= 1/6

iii. Now Cc is the complementary event of C, its probability is P(Cc)= 1 - P(C)= 1 - 1/2= 1/2

P(Cc∩Dc)= P(Cc)*P(Dc)= (1/2)*(1/3)= 1/6

vi. and e.

P(C/D)= \frac{P(CnD)}{P(D)} = \frac{1/3}{2/3} = 1/2

P(C)=1/2

As you can see the P(C)=P(C/D) ⇒ This fact proves that the events C and D are independent.

d.

i. P(C∪D)= P(C) + P(D) - P(C∩D)= 1/2 + 2/3 - 1/3= 5/6

ii. P(C∪Dc)= P(C) + P(Dc) - P(C∩Dc)= 1/2 + 1/3 - 1/6= 2/3

I hope it helps!

You might be interested in
What is the quotient of a number and 12
wolverine [178]
n-the\ number\\\\the\ quotient\ of\ a\ number\ (n)\ and\ 12=\boxed{n:12=\frac{n}{12}}
4 0
3 years ago
Heyyy!! i need friends :( im insecure ab my eyes im sorryy :(
romanna [79]

Answer:

heyoo ill be ur friend and i am sure ur eyes r beautiful

Step-by-step explanation:

4 0
3 years ago
What is the volume? <br> Find the volume?
yulyashka [42]

V≈565.49          Step-by-step explanation:

the formula for volume is PI x Raadius squared x Highth

3 0
3 years ago
A club raised 80% of its goal for a charity. The club raised $1076. What was the goal?
4vir4ik [10]

Answer:

860.8

Step-by-step explanation:

6 0
3 years ago
0.003 0.03 0.3 three more of them come after which are they ?
FromTheMoon [43]
0.3, 0.03,0.003
Because 0.3 is equivalent to 3/10
Because 0.03 is equivalent to 3/100
Because 0.003 is equivalent to 3/1000
4 0
3 years ago
Other questions:
  • Egg measures 60 minus 26.3 in around the long axis how many inches in that
    8·1 answer
  • 11/12+(−7/12). Write your answer as a fraction in simplest form.
    11·1 answer
  • A consumer takes out a loan for $500 that charges 10% annual interest. What is the total cost of the loan if the consumer pays i
    14·2 answers
  • Which triangles are similar?
    14·1 answer
  • The property tax on a $160,000 home is $3,840. At this rate, what is the property tax on a home appraised at $260,000? $
    6·1 answer
  • What are the coefficients of 4x -7 - 8x +17
    12·1 answer
  • Plsss help asap no wrong answers pls
    6·1 answer
  • Refer to the following formula for expected payoff:
    13·1 answer
  • Let f(x) = 2x - 3. If f(x) = 15, what is x?
    12·1 answer
  • I forgot how to do this please help.!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!