A batch of 400 LEDS contains 7 that are defective. This is k

Mary Keefe

Mary Keefe

Answered question

2021-12-14

A batch of 400 LEDS contains 7 that are defective. This is known to be the long-term average for the production. The company sells boxes with 50 LEDS in each box.
(a) What is the probability there are 1 or more defective bulbs in a box?
(b) If three LEDS are selected at random from a box, what is the probability that the third one selected is defective given that the first one selected was not defective and the second one selected was defective?
(c) Boxes are returned if 3 or more are defective. What is the probably a box will be returned?

Answer & Explanation

Chanell Sanborn

Chanell Sanborn

Beginner2021-12-15Added 41 answers

Step 1
Given that, in a batch of 400 LEDs 7 that are defective.
S, the probability of defective LEDs is,
P(D)=7400
=0.0175
In a box of 50 LEDs, Use binomial distribution to find the probability that there are one or more defective bulbs.
Let X be a random variable denoting the number of defective bulbs in the box.
P(X1)=1P(X=0)
=1[50C0(0.0175)0(0.982)50]
=10.403
=0.596
Therefore, the answer is 0.596.
Step 2
Part (b)
Let, X be a random variable denoting the number of defective items in the box.
Given that, three bulbs are selected at random from the box, the first one selected was not defective and second one selected was defective. So, three are3 48 remaining bulbs.
Out of these 48 remaining bulbs, the third one selected is defective is,
P(A)=48C1(0.01751)(0.98247)
=0.357
Therefore, the answer is 0.357.
Step 3
Part (c)
Given that, if three or more bulbs are defective, then, the box will be returned.
Calculate the probability that three or more bulbs are defective.
P(X3)=1[P(X=0)+P(X=1)+P(X=2)]
=1[(50C00.017500.98250)+(50C10.017510.98249)+(50C20.017520.98248)]
=1[0.403+0.359+0.181]
=10.943
=0.057
Therefore, the answer is 0.057.
Bernard Lacey

Bernard Lacey

Beginner2021-12-16Added 30 answers

Could you answer just this question, it is very necessary.
Boxes are returned if 3 or more are defective. What is the probably a box will be returned?

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