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JulijaS [17]
3 years ago
10

Suppose that the probability that any particle emitted by a radioactive material will penetrate a certain shield is 0.01. If 10

particles are emitted, what is the probability that:
a) exactly 2 of the particles will penetrate the shield?
b) How many particles must be emitted in order for the probability to be at least 0.95 that at least one particle will penetrate the shield?
Mathematics
1 answer:
AnnyKZ [126]3 years ago
4 0

Answer:

a)P=0.42

b) n\geq 297

Step-by-step explanation:

We have a binomial distribution, since the result of each experiment admits only two categories (success and failure) and the value of both possibilities is constant in all experiments. The probability of getting k successes in n trials is given by:

P=\begin{pmatrix}n\\ k\end{pmatrix} p^k(1-p)^{n-k}=\frac{n!}{k!(n!-k!)}p^k(1-p)^{n-k}

a) we have k=2, n=10 and p=0.01:

P=\frac{10!}{2!(10!-2!)}0.01^2(1-0.01)^{10-2}\\P=\frac{10!}{2!*8!}0.01^2(0.99)^{8}\\P=45*0.01^2(0.99)^8=0.42

b) We have, 1-(1-p)^n=P, Here P is the probability that at least one particle will penetrate the shield, this probabity has to be equal or greater than 0.95. Therefore, this will be equal to subtract from the total probability, the probability that the particles do not penetrate raised to the total number of particles.

1-0.99^n\geq 0.95\\0.99^n\leq 1-0.95\\0.99^n\leq 0.05\\n\geq 297

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3 0
3 years ago
The big dog weighs 5 times as much as the little dog. The little dog weighs 2 3 as much as the medium-sized dog. The medium-size
disa [49]

Answer:

The answer to your question is the big dog weighs 120 pounds

Step-by-step explanation:

Data

big dog = b    

medium dog = m

small dog = s

Equations

       b = 5s

       m = 12 + s

       s = 2/3 m

Process

1.- Substitute m in the last equation

       s = 2/3(12 + s)

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       s - 2/3s = 8

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2.- Substitute s in the first equation

        b = 5(24)

        b = 120 pounds

     

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3 years ago
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