Question

We have 4 boxes. Box one contain 2000 components of which 5% are defective. Box two contains 500 components of which 40% are defective. Box three and four contain 1000 component each with 10% defective. We select at random one of the boxes and we remove at random a single component.

Answer 1

Answer:4/35

Step-by-step explanation:

Answer 2

Answer:

For the given scenario, the prob.of getting a defective component is        16.25%

Step-by-step explanation:

As per the given data,

When we select a box at random & remove a single component at random:

        The probability of getting a defective component will depend on the box that we selected

Now ,  When we select box one, the probability of getting a defective component will be :

5%, since 5% of the components in box one are defective.

Also ,  If we select box two, the probability of getting a defective component will be :

40percent, since 40% of the components in box two are defective

Finally ,  If we select box three or four, the probability of getting a defective component will be 10%, since 10% of the components in box three and four are defective

∴ the probability of getting a defective component will depend on the box that we selected, and it can be calc. using the law of total probability_If we let D be the event that we get a defective component, and Bi be the event that we selected box i, then the probability of getting a defective component can be calculated as:

P(D) = P( D|B1 ) P( B1 ) + P( D|B2 )P(B2 ) + P(D|B3 )P(B3 ) + P(D|B4 )P(B4 )

⇒, where P(Bi) is the probability of selecting box i, which is 1/4 in this case  

Using the probabilities given in the problem

we can calculate the probability of getting a defective component as

P(D ) = 0.05 * 0.25 + 0.4 * 0.25 + 0.1 * 0.25 + 0.1 * 0.25 = 0.1625

Therefore, the probability of getting a defective component is 16.25%

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