A bag has 10 mmarbles, and 7 are black. Petra picks 2 marbles without replacing the first. What is the probability that both are black?

The probability that Petra picks two black marbles, without replacing the first one is 7/15 or 46.7%.

Step-by-step explanation:

Let's recall the formula of the probability:

Probability = Number of favorable outcomes/Total number of possible outcomes,

therefore, the probability of picking a first black marble is:

P = 7/10

now, let's find out the probability for picking a second black marble:

P = 6/9

It's different than the first one because Petra did not replace the first one.

Now, the probability that both are black is:

P = 7/10 * 6/9

P = 42/90 = 7/15

The probability that Petra picks two black marbles, without replacing the first one is 7/15 or 46.7%

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

pretty sure 750 each month!

step-by-step explanation: