I need help ASAP!!! Please i need help

A pharmacist receives a shipment of 21 bottles of a drug and has three of the bottles tested. If five of the 21 bottles are cont

blagie [28]

Answer:

The probability is 0.8722

Step-by-step explanation:

There are 21 bottles

5 of them are contaminated.

there are 21 - 5 = 16 non-contaminated bottles.

So, if we grab a bottle at random, the probability that this bottle is contaminated will be equal to the quotient between the number of contaminated bottles and the total number of bottles, this is:

p = 5/21

Now we want to find the probability that, for 3 tested bottles, that less than two (0 or 1 ) are contaminated.

Let's see each case on its own.

0 bottles:

The probability of getting a non-contaminated bottle in the first try is equal to the quotient between the number of non-contaminated bottles and the total number of bottles, this is:

p₁ = 16/21

For the second bottle is the same, but because one non-contaminated bottle was drawn before, now there are 15 non-contaminated bottles and 20 bottles in total, so now the probability is:

p₂ = 15/20

and similarly, for the third bottle the probability is:

p₃ = 14/19

The joint probability is the product of the individual probabilities, we get:

P = p₁*p₂*p₃ = (16/21)*(15/20)*(14/19) = 0.4211

Now the case that one bottle is contaminated.

Let's assume that the first one is contaminated.

The probability of getting a contaminated bottle in the first draw is equal to the quotient between the number of contaminated bottles and the total number of bottles, so:

p₁ = 5/21

For the second bottle, we want a non-contaminated one, there are 16 non-contaminated bottles and 20 bottles left, so here the probability is:

p₂ = 16/20

and for the third bottle we have the probability:

p₃ = 15/19

The joint probability is:

p = p₁*p₂*p₃ = (5/21)*(16/20)*(15/19)

Also notice that we only looked at the case where the first bottle is contaminated, we also have the case where the second one is contaminated and the case where the third one is contaminated, so there are 3 permutations, then the probability of having one contaminated bottle is:

Q = 3*p = 3*(5/21)*(16/20)*(15/19) = 0.4511

Then the probability of having less than two contaminated bottles is:

probability = P + Q = 0.4211 + 0.4511 = 0.8722

8 0

2 years ago

Simplify the following

irga5000 [103]

$\huge\fbox{Answer ☘}$

$\bold\blue{( - 8z) {}^{2} } \\\bold{ = > 64z {}^{2} }$

hope helpful~

8 0

3 years ago

What is the equation of the line that passes through the point (-3,5) and has a slope of -2

wariber [46]

Answer:

equation: y=-4x-7

Step-by-step explanation:

y=-4x+b

solve for b using given coordinates on the line (-3, 5)

5=-4(-3)+b

b=-7

6 0

3 years ago

Read 2 more answers

Parallel / Perpendicular Practice

deff fn [24]

The slope and intercept form is the form of the straight line equation that includes the value of the slope of the line

Neither
║
Neither
⊥
║
Neither
Neither
Neither

Reason:

The slope and intercept form is the form y = m·x + c

Where;

m = The slope

Two equations are parallel if their slopes are equal

Two equations are perpendicular if the relationship between their slopes, m₁, and m₂ are; $m_1 = -\dfrac{1}{m_2}$

1. The given equations are in the slope and intercept form

$\ y = 3 \cdot x + 1$

The slope, m₁ = 3

$y = \dfrac{1}{3} \cdot x + 1$

The slope, m₂ = $\dfrac{1}{3}$

Therefore, the equations are neither parallel or perpendicular

Neither

2. y = 5·x - 3

10·x - 2·y = 7

The second equation can be rewritten in the slope and intercept form as follows;

$y = 5 \cdot x -\dfrac{7}{2}$

Therefore, the two equations are parallel

║

3. The given equations are;

-2·x - 4·y = -8

-2·x + 4·y = -8

The given equations in slope and intercept form are;

$y = 2 -\dfrac{1}{2} \cdot x$

Slope, m₁ = $-\dfrac{1}{2}$

$y = \dfrac{1}{2} \cdot x - 2$

Slope, m₂ = $\dfrac{1}{2}$

The slopes

Therefore, m₁ ≠ m₂

$m_1 \neq -\dfrac{1}{m_2}$

The lines are Neither parallel nor perpendicular

Neither

4. The given equations are;

2·y - x = 2

$y = \dfrac{1}{2} \cdot x +1$

m₁ = $\dfrac{1}{2}$

y = -2·x + 4

m₂ = -2

Therefore;

$m_1 \neq -\dfrac{1}{m_2}$

Therefore, the lines are perpendicular

⊥

5. The given equations are;

4·y = 3·x + 12

-3·x + 4·y = 2

Which gives;

First equation, $y = \dfrac{3}{4} \cdot x + 3$

Second equation, $y = \dfrac{3}{4} \cdot x + \dfrac{1}{2}$

Therefore, m₁ = m₂, the lines are parallel

║

6. The given equations are;

8·x - 4·y = 16

Which gives; y = 2·x - 4

5·y - 10 = 3, therefore, y = $\dfrac{13}{5}$

Therefore, the two equations are neither parallel nor perpendicular

Neither

7. The equations are;

2·x + 6·y = -3

Which gives $y = -\dfrac{1}{3} \cdot x - \dfrac{1}{2}$

12·y = 4·x + 20

Which gives

$y = \dfrac{1}{3} \cdot x + \dfrac{5}{3}$

m₁ ≠ m₂

$m_1 \neq -\dfrac{1}{m_2}$

Neither

8. 2·x - 5·y = -3

Which gives; $y = \dfrac{2}{5} \cdot x +\dfrac{3}{5}$

5·x + 27 = 6

$x = -\dfrac{21}{5}$

Therefore, the slopes are not equal, or perpendicular, the correct option is Neither

Learn more here:

brainly.com/question/16732089

6 0

3 years ago

PLEASE HELP! I WILL GIVE BRAINLIEST! A B C D E

I am Lyosha [343]

Answer:

D

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers