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3 years ago

9

A contractor purchases a shipment of 100 transistors. It is his policy to test 10 of these transistors and to keep the shipment

only if at least 9 of the 10 are in working condition. If the shipment contains 20 defective transistors, what is the probability it will be kept?

1 answer:

Serjik [45]3 years ago

4 0

Answer:

Hence the probability of the at least 9 of 10 in working condition is 0.3630492

Step-by-step explanation:

Given:

total transistors=100

defective=20

To Find:

P(X≥9)=P(X=9)+P(X=10)

Solution:

There are 20 defective and 80 working transistors.

Probability of at least 9 of 10 should be working out 80 working transistors

is given by,

P(X≥9)=P(X=9)+P(X=10)

<em>{80C9 gives set of working transistor and 20C1 gives 20 defective transistor and 100C10 is combination of shipment of 10 transistors}</em>

P(X≥9)= ${80C9*20C(10-9)}/(100C10)+{80C10*20(10-10)}/(100C10)$

<em>(Use the permutation and combination calculator)</em>

P(X≥9)=(231900297200*20/17310309456440)

+(1646492110120/17310309456440)

P(X≥9)=0.267933+0.0951162

P(X≥9)=0.3630492

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Answer:

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Step-by-step explanation:

<u>According to the Figure Given:</u>

Total Horizontal Distance = 14 in

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<u>To Find :</u>

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<u>Solution:</u>

Firstly we need to find the area of Rectangular part.

So We know that,

$\boxed{ \rm \: Area \: of \: Rectangle = Length×Breadth}$

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$\boxed{\rm \: Breadth = total \: distance - Radius}$

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Hence, the Breadth is 8 in.

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Then, We need to find the area of Quarter circle :

We know that,

$\boxed{\rm Area_{(Quarter \; Circle) } = \cfrac{\pi{r} {}^{2} }{4}}$

Now Substitute their values:

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$\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 6 {}^{2} }{4}$

Solve it.

$\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 36}{4}$

$\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times \cancel{{36} } \: ^{9} }{ \cancel4}$

$\longrightarrow\rm Area_{(Quarter \; Circle)} =3.14 \times 9$

$\longrightarrow\rm Area_{(Quarter \; Circle) } = 28.26 \: {in}^{2}$

Now we can Find out the total Area of composite figure:

We know that,

$\boxed{ \rm \: Area_{(Composite Figure)} =Area_{(rectangle)}+ Area_{ (Quarter Circle)}}$

So Substitute their values:

$\rm Area_{(rectangle)}$ = 48
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$\longrightarrow \rm \: Area_{(Composite Figure)} =48 + 28 .26$

Solve it.

$\longrightarrow \rm \: Area_{(Composite Figure)} =\boxed{\tt 76.26 \:\rm in {}^{2}}$

Hence, the area of the composite figure would be 76.26 in² or 76.26 sq. in.

$\rule{225pt}{2pt}$

I hope this helps!

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