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
If T(n) = 6n - 1 what is the 1st term
Nataliya [291]
T(n) = 6n - 1
T(1) = 6(1) - 1
T(n) = 6 - 1
T(n) = 5
3 0
3 years ago
Help pls thank you.............
Elenna [48]

Answer:

15\lb of course

Step-by-step explanation:

all u do is subtract the rate of change an youll get your answer

3 0
3 years ago
Read 2 more answers
15 is what percent of 40?<br><br> Pls Show Work<br><br> Thx
Free_Kalibri [48]
15 = rate * 40
rate = 15/40
rate = 0.375 * 100% = 37.5%
4 0
3 years ago
Read 2 more answers
Kelly took 12 pictures at school on Tuesday. She took 7 pictures at lunch and 5 pictures at recess. If she randomly selects a pi
goblinko [34]
D.  5/12 is your answer
3 0
3 years ago
What is the slope of line b?
Semmy [17]

Answer:

It is c)1/2

Step-by-step explanation:

Since its rising its postive

And the rise is 1 and the run is 2 so the slope is 1/2

3 0
2 years ago
Read 2 more answers
Other questions:
  • Match each point with one of the following fractions 5/6, 7/12, 1/8, 5/16
    8·2 answers
  • I need the answer pls pls pls answer pls
    6·1 answer
  • EASY GEOMETRY**<br>name a right angle on the figure ​
    12·1 answer
  • PLEASE HELP ME!!!! ASAP PLEASE!
    11·1 answer
  • What is another way to write 4 hundreds
    12·2 answers
  • Solve the problem please
    10·2 answers
  • If a and b are the zeros of the quadratic polynomial 4x2+4x+1, find the value of a/b+b/a?
    12·1 answer
  • I need help anyoneeeeeee
    6·1 answer
  • This alfebra problem
    6·1 answer
  • Work out the area of the shaded shape
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!