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
matrenka [14]
2 years ago
7

For each set of probabilities, determine whether the events A and B are independent or dependent.

Mathematics
1 answer:
lozanna [386]2 years ago
7 0

Answers:

  • (a) Independent
  • (b) Dependent
  • (c) Dependent
  • (d) Independent

========================================================

Explanation:

If events A and B are independent, then the two following equations must both be true

  • P(A | B) = P(A)
  • P(B | A) = P(B)

This is because the conditional probability P(A|B) means "P(A) when B has happened". If B were to happen, then P(A) must be the same as before. In other words, event B does not affect A, and vice versa.

For part (a), we have P(B) = 1/4 and P(B|A) = 1/4 showing that P(B|A) = P(B) is true, and therefore we can say the events are independent. We don't need the info that P(A) = 1/8.

------------------------

Unlike part (a), part (b) has the answer "dependent" because P(A) = 1/8 and P(A | B) = 1/3 differ in value. Event A starts off at probability 1/8, but then event B occurring means P(A) gets increased to 1/3. The prior knowledge about B changes the chances of A. The P(B) = 1/5 is unneeded.

------------------------

If A and B were independent, then,

P(A and B) = P(A)*P(B)

However,

P(A)*P(B) = (1/4)*(1/5) = 1/20

which is not the same as P(A and B) = 1/6. Therefore the two events are dependent.

------------------------

Refer back to part (a)

P(A) = 1/4 and P(A|B) = 1/4 are identical in value, so P(A|B) = P(A) which leads to the events being independent. Whether we know event B happened or not, it does not affect the outcome of event A. P(B) = 1/9 is unneeded.

You might be interested in
What is the x-value of the solution to the system of equations?
ValentinkaMS [17]

Answer:

The solution to the system of equations is:

x=4,\:y=-3

Step-by-step explanation:

Given the system of equations

5x + 4y =8

2x- 3y = 17

solving the system of equations

\begin{bmatrix}5x+4y=8\\ 2x-3y=17\end{bmatrix}

\mathrm{Multiply\:}5x+4y=8\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:10x+8y=16

\mathrm{Multiply\:}2x-3y=17\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:10x-15y=85

\begin{bmatrix}10x+8y=16\\ 10x-15y=85\end{bmatrix}

10x-15y=85

-

\underline{10x+8y=16}

-23y=69

\begin{bmatrix}10x+8y=16\\ -23y=69\end{bmatrix}

solve for y

-23y=69

Divide both sides by -23

\frac{-23y}{-23}=\frac{69}{-23}

y=-3

\mathrm{For\:}10x+8y=16\mathrm{\:plug\:in\:}y=-3

10x+8\left(-3\right)=16

10x-24=16

10x=40

Divide both sides by 10

\frac{10x}{10}=\frac{40}{10}

x=4

Thus, the solution to the system of equations is:

x=4,\:y=-3

7 0
3 years ago
10 points pls answer ASAP
boyakko [2]

Answer:

145

Step-by-step explanation:

Its the opposite angle of 145

7 0
3 years ago
(6m^2-2-5+m)-(3m-4+11m^2)
Murljashka [212]

(6m^2-2-5+m)-(3m-4+11m^2) =

<h2>6m^2 - 2m - 124</h2>
7 0
3 years ago
Determine whether QRS is a right triangle for the given vertices. Explain.
LekaFEV [45]

Answer:

B

Step-by-step explanation:

6 0
3 years ago
Need the answers for 3-5
nevsk [136]

Answer:

k12

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • .....................................
    10·1 answer
  • Which one of the following tin-lead soldiers has the lowest melting point?        A. 60/40   B. 70/30   C. 40/60   D. 50/50  
    8·1 answer
  • oindexter has a credit card that uses the average daily balance method. For the first 15 days of a 31-day billing cycle, his bal
    9·2 answers
  • This data represents the number of oil changes completed each day last week at Jeff's Auto Center. 19, 16, 24, 12, 16, 21, 18 Wh
    6·1 answer
  • The upper-left coordinates on a rectangle are (-4,4), and the upper-right coordinates are (4,4).The rectangle has an area of 8 s
    12·2 answers
  • A mahogany desk with a cash price of $810 is offered on the installment plan at $50 down and $58 per month for 15 months. what i
    6·1 answer
  • How to make number set 11 to 15
    14·1 answer
  • Graph the equation. y=3(x+1)^2-2 <br> HELP!!
    8·1 answer
  • I'm not exactly sure what I'm supposed to be doing, so if someone could help me out. That'd be great.
    8·1 answer
  • Find the sum of the infinite geometric sequence that begins 1/12, 1/18, 1/27, …
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!