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

Answer:

a) Figure attached

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

Step-by-step explanation:

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

$P(D) = \frac{1000}{10000}=0.1$

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.

Answer 2

The probability that both switches are defective is 1%.

Given that a shipment contains 10,000 switches, and of these, 1000 are bad, and an inspector draws 2 switches at random, one after the other, to find the probability that both switches are defective the following calculation must be performed:

• 1000/10000 = 1/10
• 1/10 x 1/10 = X
• 0.1 x 0.1 = X
• 0.01 = X
• 0.01 x 100 = 1

Therefore, the probability that both switches are defective is 1%.

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