Ask question

Ask question

All categories

4 years ago

14

There are 2 red and 5 green balls in a bag. If you randomly choose balls one at a time , with replacement , What is the probabil

ity of choosing 2 green balls and then 1 red ball?
A. 2/21
B.20/147
C.50/343
D. 5/21

2 answers:

Nikolay [14]4 years ago

8 0

Option C

<u>ANSWER: </u>

The probability of choosing 2 green balls and 1 red ball is $\frac{50}{343}$

<u>SOLUTION: </u>

Given, there are 2 red and 5 green balls in a bag.

So, there are 7 balls in the bag.

We need to find the probability of choosing 2 green balls and 1 red ball.

Probability of 2 green balls and 1 red ball = probability of 1st green ball $\times$ probability of 2nd green ball x probability of 1 red ball.

Now, probability of 1st green ball = $\frac{\text {number of green balls}}{\text {total number of balls}}$

= $\frac{5}{7}$

because we are replacing after every pick.

Now, probability of red ball = $\frac{\text {number of red balls}}{\text {total number of balls}}$

$=\frac{2}{7}$

Probability of 2 green balls and 1 red ball = $\frac{5}{7} \times \frac{5}{7} \times \frac{2}{7}$

$=\frac{5 \times 5 \times 2}{7 \times 7 \times 7}$

$=\frac{50}{343}$

Hence, the probability of choosing 2 green balls and 1 red ball is $\frac{50}{343}$

Musya8 [376]4 years ago

4 0

Answer:

D is the answer

Step-by-step explanation:

You might be interested in

Help please, I will give brain list

lara [203]

A=WL
115=5L
Divide by 5
23=L

5 0

3 years ago

According to a Los Angeles Times study of more than 1 million medical dispatches from to , the response time for medical aid var

-BARSIC- [3]

Answer:

A)Mean :10.65

Median =10.7

Mode : 10.7

B)Range = 3.5

Standard deviation :0.89916

C)The response time of 8.3 minutes should be considered an outlier in comparison to the other response times

Step-by-step explanation:

A)

Data : 11.8 ,10.3, 10.7, 10.6, 11.5, 8.3, 10.5, 10.9, 10.7, 11.2

$Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{11.8 +10.3+ 10.7+ 10.6+ 11.5+ 8.3+ 10.5+ 10.9+ 10.7+ 11.2}{10}$

Mean = 10.65

Median: The mid value of the data

Data in ascending order

8.3

10.3

10.5

10.6

10.7

10.7

10.9

11.2

11.5

11.8

n=10(even)

$Median = \frac{(\frac{n}{2})\text{th term}+(\frac{n}{2}+1)\text{th term}}{2}\\Median = \frac{(\frac{10}{2})\text{th term}+(\frac{10}{2}+1)\text{th term}}{2}\\Median = \frac{10.7+10.7}{2}\\Median = 10.7$

Mode : the most occurring frequency

10.7 is occurring twice while others are occurring once

So, Mode is 10.7

B) Range = Maximum - Minimum=11.8-8.3=3.5

Standard deviation : $\sqrt{\frac{\sum(x-\bar{x})^2}{n}}$

Standard deviation : $\sqrt{\frac{(11.8-10.65)^2+(10.3-10.65)^2+......+(10.9-10.65)^2+(10.7-10.65)^2+(11.2-10.65)^2}{10}}$

Standard deviation :0.89916

C)

8.3

,10.3

,10.5

,10.6

,10.7

,10.7

,10.9

,11.2

,11.5

,11.8

For Q1 ( Median of lower quartile )

8.3

,10.3

,10.5

,10.6

,10.7

$Median = \frac{n+1}{2}\text{th term} =\frac{5+1}{2}=3 \text{rd term}=10.5$

For Q3( Median of Upper quartile )

10.7

,10.9

,11.2

,11.5

,11.8

$Median = \frac{n+1}{2}\text{th term} =\frac{5+1}{2}=3 \text{rd term}=11.2$

IQR = Q3-Q1=11.2-10.5=0.7

Range :(Q1-1.5IQR, Q3-1.5IQR)

Range : $(10.5-1.5 \times 0.7, 11.2-1.5 \times 0.7)$

Range :(9.45, 10.15)

8.3 does not lie in this interval

So, the response time of 8.3 minutes should be considered an outlier in comparison to the other response times

3 0

3 years ago

Combine like terms to simplify the expression: 7 − x − 4

9966 [12]

Answer:

3 + (-x) or -x + 3 they are the same just different ways to write them.

Step-by-step explanation:

7 - 4 = 3

there is only one variable so -x stays the same.

7 0

3 years ago

Will mark brainliest! Can something pls help me answer these showing there work? I offer 15 points

wariber [46]

Answer:

a) Third Quadrant

b) 7π/4 --> Option (4)

c) $-\frac{\sqrt{3} }{2}$ --> Option (1)

d) 1 --> Option (1)

e) $\frac{\sqrt{2} }{2}$ --> Option (2)

f) - $\frac{1}{2}$ --> Option (2)

g) $\frac{3}{2}$ --> Option (1)

h) $-\frac{\sqrt{3} }{2}$ --> Option(2)

Step-by-step explanation:

Ok, lets properly define some technical term here.

The terminal side of an angle is the side of the line after that it has made a turn (angle). I will drive my point home with the attachment to this solution

The initial side of an angle is the side of the line before the line made a turn(angle)

a) 1 complete revolution = $360^{0}$ = 2π rads

we can convert the radians to degrees using the above conversion rate

=> $\frac{7π}{6} rad \to degrees$ will be: $\frac{\frac{7π}{6} * 360}{2π}$

solving the expression above, 420π/2π = $210^{0}$

From the value of the angle in degree and having in mind that

$0^{0} - 90^{0} \to first \ quadrant\\ \\91^{0} - 180^{0} \to second\ quadrant\\\\181^{0} - 270^{0} \to third\ quadrant\\\\271^{0} - 360^{0} \to fourth\ quadrant$

$\frac{7π}{6} rad = 210^{0} \ is \ in \ third \ quadrant\\$

b) Co-terminal angles are angles which share the same initial and terminal side

To find the co-terminal of an angle we add or subtract 360 to the value if in degrees or 2π if in radians. From the value we want to find its co-terminal, because of the presence of π, its value is in radians and as such we add or subtract 2π from the value. If we perform subtraction, the negative co-terminal of the angle has been evaluated and the positive co-terminal is evaluated if we perform addition.

So, to get the positive co-terminal of -π/4, we add 2π and doing that, we get:

2π - π/4 = 7π/4

c) The value of sin(π/3) * cos(π) is ?

Applying special angle properties: (More on the special angle in the diagram attached to this solution)

sin(π/3) = $\frac{\sqrt{3} }{2}$

cos(π) = -1

substituting the values above into the expression, we have:

$\frac{\sqrt{3} }{2} * -1 = -\frac{\sqrt{3} }{2}$

d) if $f(x) = sin^{2}x + cos^{2} x$ , f(π/4) = ?

In trignometry, $sin^{2}x = (sin(x))^{2} ;\ cos^{2}x = (cos(x))^{2}$

Applying special angle properties again,

sin(π/4) = $\frac{\sqrt{2} }{2}$

cos(π/4) = $\frac{\sqrt{2} }{2}$

The expression becomes $(\frac{\sqrt{2} }{2} )^{2} + (\frac{\sqrt{2} }{2} )^{2}$ . Simplifying, we get:

2/4 + 2/4 = 1/2 + 1/2 = 1

e) cos(3π/4)

3π/4 is not an acute angle(angle < less than π/2 rad) and as such, we need to get its related acute angle. Now 3π/4 rads is in the second quadrant, this means that we will have to subtract 3π/4 from π to get the related acute angle.

π - 3π/4 = π/4

so instead of working with 3π/4, we work with its related acute angle which is π/4

cos(3π/4) is equivalent to cos(π/4) = $\frac{\sqrt{2} }{2}$ (special angle properties)

f) sin(11π/6)

11π/6 is not an acute angle(angle less than π/2 rad) and it is in the fourth quadrant. This means that to get its related acute angle, we have to subtract it from 2π

2π - 11π/6 = π/6

sin(11π/6) is equivalent to -sin(π/6) = -1/2 (special angle properties).

Note that there is a minus in the answer. That had nothing to do with the special angle properties but rather, the fact that:

At the fourth quadrant, only the cosine trignometric ratio is positive
At the first quadrant, all trignometric ratios are positive
At the second quadrant, only the sine trignometric ratio is positive
At the third quadrant, only the tangent trignometric ratio is positive

g) sin(π/6) + tan(π/4)

using special angle properties:

sin(π/6) = 1/2 and tan(π/4) = 1

the expression simplifies to: 1/2+1 = 3/2

h) cos(4π/3)

4π/3 is not an acute angle and it is in the third quadrant

To get its related acute angle, we have to subtract it from 3π/2

3π/2 - 4π/3 = π/6

so, cos(4π/3) = -cos(π/6) (The negative value is because of the fact that at the third quadrant, only the tangent trignometric ratio is positive)

using special angle properties, -cos(π/6) = $-\frac{\sqrt{3} }{2}$

7 0

3 years ago

Each cube in the prisms below has a volume of 1 cubic unit. which prism has a volume of 60 cubic units

mr_godi [17]

For A, 5x4x3=60
for B 5x3x2=30
for C 5x4x1=20
for D 5x4x2=40
hence, A has a volume of 60cubic units!

7 0

4 years ago