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Citrus2011 [14]
3 years ago
13

According to police sources, a car with a certain protection system will be recovered 87% of the time. Find the probability that

4 of 8 stolen cars will be recovered?
Mathematics
1 answer:
WITCHER [35]3 years ago
5 0

Answer: 0.01145

Step-by-step explanation:

We use Binomial distribution , where the probability of getting x successes in n trial is given by :-

P(x)=^nC_xp^x(1-p)^{n-x} , p = probability of getting each success in each trial.

As per given

The proportion that a car with a certain protection system will be recovered= p=0.87

n= 8

Let x be the number of cars will be recovered.

Then, the probability that 4 of 8 stolen cars will be recovered:

P(X=4)=^8C_4(0.87)^4(1-0.87)^{8-4}

=\dfrac{8!}{4!(8-4)!}(0.87)^4(0.13)^4\\\\= 70(0.57289761)(0.00028561)\\\\=0.0114537700474\approx0.01145

Hence, the required probability is 0.01145.

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8 0
3 years ago
An instructor wants to write a test with 25 questions where each question is worth 3, 4, or 5 points based on difficulty. He wan
irakobra [83]

ANSWER

Find out the how many 3, 4, and 5 point questions could there be.

To proof

Let us assume that the 3 points based question be = x

Let us assume that the 4 points based question be = y

Let us assume that the 5 points based question be = z

As given

An instructor wants to write a test with 25 questions

than the equation become in the form

x + y + z = 25

he quiz to be worth a total of 100 points.

than the equation is becomes

3x + 4y + 5z =100

As given

He wants the number of 3-point questions to be 4 less than the number of 4-point questions

x = y -4

Than the three equation are

x + y + z = 25 ,3x + 4y + 5z =100 and x = y -4

put  x = y -4 in the x + y + z = 25 ,3x + 4y + 5z =100

than

2y + z = 29, 7y +5z= 112

multiply 2y + z = 29 by 5 and subtracted 7y +5z= 112

10 y -7y + 5y -5y = 145 -112

3y = 33

y = \frac{33}{3}

y =11

put in the  x = y -4

x = 11-4

x= 7

put the value of x ,y in the x + y + z = 25

7 + 11 +z =25

18 +z = 25

z = 25 -18

z=7

therefore

numbers of the 3 point question be = 7

numbers of the 4 point question be = 11

numbers of the 5 point question be = 7

Hence proved



3 0
3 years ago
Find the value of x.​
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Answer:

the value of x is 150° because all are 150°

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2 years ago
Bert can paddle his kayak at a maximum speed of 270metersperminute. If he paddles across a lake at one-third of his top speed fo
nikdorinn [45]

Answer:

4

Step-by-step explanation:

8 0
2 years ago
A shipment of 24 electric typewriters are rejected if 3 are checked for defects and at least 1 is found to be defective. Find th
Maslowich

Answer:

You keep them if you test 3 and all pass.

There are 18 good ones and 6 bad (making 24)

Chance of first passing is 18/24

If it passes, there are now one less good and one less total.

Chance of second passing is 17/23

If it passes, there are now one less good and one less total.

Chance of second passing is 16/22

Total is (16 x 17 x 18) / (22 x 23 x 24) = about 0.4 (0.403162055 is you really want to know).

So probability all are ok is 0.4

Thus probability you find at least one bad one is 0.6

Hope this helps you out!

8 0
3 years ago
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