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
LenaWriter [7]
3 years ago
12

An urn contains 5 white and 10 black balls. A fair die is rolled and that number of balls is randomly chosen from the urn. What

is the probability that all of the balls selected are white? What is the conditional probability that the die landed on 3 if all the balls selected are white?
Mathematics
1 answer:
galina1969 [7]3 years ago
7 0

Answer:

Part A:

The probability that all of the balls selected are white:

P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\      P(A)=\frac{5}{66}=0.075757576

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516

Step-by-step explanation:

A is the event all balls are white.

D_i is the dice outcome.

Sine the die is fair:

P(D_i)=\frac{1}{6} for i∈{1,2,3,4,5,6}

In case of 10 black and 5 white balls:

P(A|D_1)=\frac{5_{C}_1}{15_{C}_1} =\frac{5}{15}=\frac{1}{3}

P(A|D_2)=\frac{5_{C}_2}{15_{C}_2} =\frac{10}{105}=\frac{2}{21}

P(A|D_3)=\frac{5_{C}_3}{15_{C}_3} =\frac{10}{455}=\frac{2}{91}

P(A|D_4)=\frac{5_{C}_4}{15_{C}_4} =\frac{5}{1365}=\frac{1}{273}

P(A|D_5)=\frac{5_{C}_5}{15_{C}_5} =\frac{1}{3003}=\frac{1}{3003}

P(A|D_6)=\frac{5_{C}_6}{15_{C}_6} =0

Part A:

The probability that all of the balls selected are white:

P(A)=\sum^6_{i=1} P(A|D_i)P(D_i)

P(A)=\frac{1}{6}(\frac{1}{3}+\frac{2}{21}+\frac{2}{91}+\frac{1}{273}+\frac{1}{3003}+0)\\      P(A)=\frac{5}{66}=0.075757576

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

We have to find P(D_3|A)

The data required is calculated above:

P(D_3|A)=\frac{P(A|D_3)P(D_3)}{P(A)}\\ P(D_3|A)=\frac{\frac{2}{91}*\frac{1}{6}}{\frac{5}{66} } \\P(D_3|A)=\frac{22}{455}=0.0483516

You might be interested in
Use the given conditions to write an equation for the line in​ point-slope form and general form. Passing through (8 comma negat
miskamm [114]

Answer:

The answer to your question is   y = -5x + 32          point-slope form

                                                      5x + y - 32 = 0      general form

Step-by-step explanation:

Data

(8, -8)

⊥ x - 5y - 6 = 0

Process

1.- Get the slope of the line given

   x - 5y - 6 = 0

   -5y = -x + 6

      y = -x/-5 + 6/-5

      y = x/5 - 6/5

slope = 1/5

slope of the new line -5, because the lines are perpendicular

2.- Get the equation of the new line

          y - y1 = m(x - x1)

          y + 8 = -5(x - 8)

          y + 8 = -5x + 40

          y = -5x + 40 - 8

         y = -5x + 32          point-slope form

Equal to zero to find the general form

         5x + y - 32 = 0      general form

5 0
3 years ago
Rigid motion transformations produce images that:
igomit [66]

C. Moved to a different location but congruent in size and shape.

Rigid motion transformations are when a shape is moved, rotated, reflected, or any other type of transformation but the size and shape stay the same.

Non-rigid is when an object is moved but the size and shape can change.

Hope this helps :))

5 0
3 years ago
Drag a vertex of the triangle to change its shape.
likoan [24]

Answer:

The correct option is;

45°

Step-by-step explanation:

By angle sum theorem, we have that the sum of angles in a triangle = 180°

Therefore, we have;

When the interior angles of the triangle are constructed to be 60° and 75°, we have by the angle sum theorem;

The third angle + 60° + 75° = 180°

Which gives;

The third angle  = 180°- 60° - 75° = 180°- 135° = 45°

The measurement of the third angle by the angle sum theorem will be 45°

The correct option is ∠third angle = 45°.

8 0
3 years ago
-3y-2=7 what is the value of y
tiny-mole [99]

Answer:

y = -3

Step-by-step explanation:

Add 2 to each side to isolate the -3y. Doing this leaves you with -3y=9. You then divide each side leaving you with y = -3

6 0
3 years ago
Read 2 more answers
Write each equation in slope-intercept form. Identify the slope and y-intercept. Then graph the line described by the question.
Rasek [7]

Answer:

Step-by-step explanation:

Equation of the line is,

y = -x + 2

By comparing this equation with,

y = mx + b

Here, m = slope of the line

b = y-intercept

Therefore, slope of the line given in the graph = (-1)

y-intercept = 2

Now we will find the table for the points lying on the line,

x       -6          -4           0           4            6

y        8           6           2          -2           -4

Now plot these points on the graph and join them to get the line.

6 0
3 years ago
Other questions:
  • The ages of Edna, Ellie, and Elsa are consecutive integers. The sum of their ages is 108. What are their ages?
    7·1 answer
  • Pllzzzz Help Is Needed.
    8·1 answer
  • What is the mean number of points<br> scored by these players? D A. 7 B. &amp; DD. 10​
    8·1 answer
  • What is most likely true about the population of 250 grand parents
    12·2 answers
  • Identify the hypothesis and conclusion of each conditional statement. Then write each sentence in if-then form
    10·1 answer
  • Larry rides his bike 5/6 mile 4 times a week. How far does Larry ride his bike each week?
    7·2 answers
  • Helppppppppppppppppppppp​
    13·2 answers
  • Please help I’ll mark as brainliest
    6·1 answer
  • WILL GIVE BRAINLIEST!!
    5·2 answers
  • Thad attempted 25 free throws and made 17 of them while Amy attempted 30 and may 20. Who shot the higher percentage
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!