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Brums [2.3K]
3 years ago
13

Your neighbor has a bag with 5 oranges and 7 apples in it. You will be receiving two pieces of fruit from your neighbor. What is

the probability, in percent, that you will receive 2 apples, assuming she removes them from the bag in random order
Mathematics
1 answer:
Snezhnost [94]3 years ago
4 0

Answer:

31.82% probability that you will receive 2 apples.

Step-by-step explanation:

The fruits are removed from the bag, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

In this question:

5 + 7 = 12 total fruits, which means that N = 12

7 apples, which means that k = 7

You receive 2 fruits, which means that n = 2

What is the probability, in percent, that you will receive 2 apples, assuming she removes them from the bag in random order?

This is, as a proportion, P(X = 2). So

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 2) = h(2,12,2,7) = \frac{C_{7,2}*C_{5,0}}{C_{12,2}} = 0.3182

0.3182*100% = 31.82%

31.82% probability that you will receive 2 apples.

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hammer [34]

Answer:

1st pic answer:

Slope= -3

Parallel slope= -3

Perpendicular slope = 1/3

2nd pic answers:

1 and 2 are parallel

1 and 3 are perpendicular

2 and 3 are perpendicular

Step-by-step explanation:

To find the slope in your first equation (6x+2y=1) you need to get y alone so that your equation will be in slope-intercept form (y=mx+b).

6x+2y=1     Start by subtracting the 6x over to the other side.

-6x      -6x

2y= -6x+1   Next divide by 2 to get y completely alone.

\frac{2y}{2} =\frac{-6x}{2}+\frac{1}{2}

y= -3x+1/2

So to answer the first part your slope is -3. Parallel slope would be the same as your regular slope. Perpendicular would be the opposite, so that means you have to flip it and change the sign.

-3 flipped is -1/3

if you change the sign it becomes positive giving you 1/3

Part 2

Your first step would be to get all the equations into the slope-intercept form (y=mx+b). The second one is already in the form so we only need to change 1 and 3.

3y=5x+2   To get y alone you need to divide everything by 3.

\frac{3y}{3}=\frac{5x}{3} +\frac{2}{3}

y=5/3x+2/3  Before we work on equation 3 we can go ahead and compare equations 1 and 2.

1: y=\frac{5x}{3} +\frac{2}{3}

2: y=\frac{5x}{3} +7   Since 1 and 2 have the same slope they would be parallel.

Now to change equation 3.

6x+10y=8    Start by subtracting the 6x over to the other side.

-6x       -6x

10y=-6x+8     Now divide everything by 10 to get y alone.

\frac{10y}{10}=\frac{-6x}{10} +\frac{8}{10}

y=-6x/10+8/10   Now we need to simplify the fractions using common factors. I'm going to use 2 for both equations, so you take -6 and 10 both divided by 2, which gives you -3 and 5(-3x/5). Now do the same with the other fraction. 8 and 10 divided by 2 gives us 4 and 5 (4/5)

3: y=\frac{-3x}{5}+\frac{4}{5}

2: y=\frac{5x}{3} +7

1: y=\frac{5x}{3} +\frac{2}{3}

Since three has an opposite slope of both 1 and 2 it would be perpendicular to both.

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Step-by-step explanation:

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