Inspecting switches a shipment contains 10,000 switches. of these, 1000 are bad. an inspector draws 2 switches at random, one after the other. a) draw a tree diagram that shows the sample space of this chance process. b) find the probability that both switches are defective.

a) Figure attached

b)

Step-by-step explanation:

For this case we can find first the probability of being dfective on the shipment like this:

Since he select 10000 and 1000 of theme were defective.

Now we know that the inspector select 2 switches at random so then we can create the possible outcomes.

Part a

The tree diagram is on the figure attached, the sample space on this case is:

D = represent a defective switch

N= represent a non defective swicth

Part b

For this case we want the probability that both switches would be defective and on this case we can do this:

Assuming independent between the events.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

the answer is b.

step-by-step explanation: