Question

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.

Answer 1

a) Figure attached

b)
`P(DD) =0.1*0.1= 0.01`

Explanation:

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

`P(D) = (1000)/(10000)=0.1`

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:

`S=[DN , DD, NN, ND]`

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:

`P(DD) =0.1*0.1= 0.01`

Assuming independent between the events.