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
Nataliya [291]
3 years ago
7

Seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and 18 green balls. Find the probability that (a)

3 red, 2 blue, and 2 green balls are withdrawn; (b) at least 2 red balls are withdrawn; (c) all withdrawn balls are the same color; (d) either exactly 3 red balls or exactly 3 blue balls are withdrawn.
Mathematics
1 answer:
UNO [17]3 years ago
8 0

Answer:

a) P=0.226

b) P=0.6

c) P=0.0008

d) P=0.74

Step-by-step explanation:

We know that the seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and 18 green balls. Therefore, we have 46 balls.

a) We calculate the probability that are 3 red, 2 blue, and 2 green balls.

We calculate the number of possible combinations:

C_7^{46}=\frac{46!}{7!(46-7)!}=53524680

We calculate the number of favorable combinations:

C_3^{12}\cdot C_2^{16}\cdot C_2^{18}=660\cdot 120\cdot 153=12117600

Therefore, the probability is

P=\frac{12117600}{53524680}\\\\P=0.226

b) We calculate the probability that are at least 2 red balls.

We calculate the probability  withdrawn of 1 or none of the red balls.

We calculate the number of possible combinations:

C_7^{46}=\frac{46!}{7!(46-7)!}=53524680

We calculate the number of favorable combinations: for 1 red balls

C_1^{12}\cdot C_7^{34}=12\cdot 1344904=16138848

Therefore, the probability is

P_1=\frac{16138848}{53524680}\\\\P_1=0.3

We calculate the number of favorable combinations: for none red balls

C_7^{34}=5379616

Therefore, the probability is

P_0=\frac{5379616}{53524680}\\\\P_0=0.1

Therefore, the  the probability that are at least 2 red balls is

P=1-P_1-P_0\\\\P=1-0.3-0.1\\\\P=0.6

c) We calculate the probability that are all withdrawn balls are the same color.

We calculate the number of possible combinations:

C_7^{46}=\frac{46!}{7!(46-7)!}=53524680

We calculate the number of favorable combinations:

C_7^{12}+C_7^{16}+C_7^{18}=792+11440+31824=44056

Therefore, the probability is

P=\frac{44056}{53524680}\\\\P=0.0008

d) We calculate the probability that are either exactly 3 red balls or exactly 3 blue balls are withdrawn.

Let X, event that exactly 3 red balls selected.

P(X)=\frac{C_3^{12}\cdot C_4^{34}}{53524680}=0.57\\

Let Y, event that exactly 3 blue balls selected.

P(Y)=\frac{C_3^{16}\cdot C_4^{30}}{53524680}=0.29\\

We have

P(X\cap Y)=\frac{18\cdot C_3^{12} C_3^{16}}{53524680}=0.12

Therefore, we get

P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)\\\\P(X\cup Y)=0.57+0.29-0.12\\\\P(X\cup Y)=0.74

You might be interested in
Mr. Chase is having a party for his teachers. If the pizzeria cuts their pies into eight slices and each teacher is eating 1/8 o
Ivanshal [37]
6 pies.

If 8 teachers finish one whole pie, and they need to feed 47, then they need 6 pies with 8 slices each aka 48 slices total, there will be one slice leftover for the principal :D
6 0
2 years ago
Lin's teacher uses the box to store her set of cubes with an edge length of one half inch. if the box is completely full, how ma
nlexa [21]

Answer:

448 cubes

Step-by-step explanation:

Volume of cubes fitted in the box will be equal to the cumulative volume of the cubes.

Since, volume of a cube = (Side)³

Side of the cube = \frac{1}{2} inch

Therefore, volume of the cube = (\frac{1}{2})^3=\frac{1}{8} inches

Volume of the storage box = 56 cubic inches

Since, number of cubes fitted in the storage box = \frac{\text{Volume of the storage box}}{\text{Volume of one cube}}

                                                                                 = \frac{56}{\frac{1}{8}}

                                                                                 = 56 × 8

                                                                                 = 448 cubes

Therefore, number of cubes fitted in the storage box = 448

3 0
3 years ago
What is the value of n 9 times 27+2 times31-28
Kay [80]
9•27+2•31-28= ? Is that what you are asking?
8 0
3 years ago
Zhane picked 28 cherries. 1/7 of them are bad. How many groups of cherries would she have to divide them into to find out how ma
castortr0y [4]
She would have 7 groups of cherries
4 0
3 years ago
a line has the equation 8x-2y=24 in standard form.Rewrite the equation of the line in slope intercept form.Then report the slope
inna [77]
8x-2y=24
-8x     -8x
-2y=-8x+24
----- ---- ----
  -2   -2   -2
y=4x-12

slope: 4
y-intercept: -12

6 0
3 years ago
Other questions:
  • (50 POINTS)Describe the transformation that maps the pre-image A to the image A'.
    7·1 answer
  • Given m || n, find x.
    14·1 answer
  • You earn $5 for every friendship bracelet you sell. Right and solve an equation to find the number of bracelets you have to sell
    6·1 answer
  • What’s the answer of 2w+-4•6
    9·1 answer
  • What is the solution of a linear system?
    9·1 answer
  • Find simple interest <br>Rs.6500 for 2years 3months at<br>6percent per annum<br><br>​
    6·1 answer
  • What is the value of y for the line when x=-4
    12·1 answer
  • F(x) = 3 x² + 5 x - 7 and g(x) = x² + 8 x + 10
    7·1 answer
  • 30x^3 + 20x^2 - 45 - 30 *
    11·1 answer
  • 17 There are 64 species of animals in the Metropolitan Zoo.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!