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The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 50 trials and got the following results.Outcome 0 1 2 3 4 5 6 7 8 9Number of Trals 5 9 4 7 5 1 8 2 2 7Fill in the table below. Round your answers to the nearest thousandth.() Assuming that the machine is falr, compute the theoretical probability of getting a 6.0(b) From these results, compute the experimental probability of getting a 6.(C) Assuming that the machine is fair, choose the statement below that is true:with a large number of trials, there must be no difference between the experimentaland theoretical probabilities.With a large number of trials, there might be a difference between the experimentaland theoretical probabilities, but the difference should be smallwith a large number of trials, there must be a large difference between theexperimental and theoretical probabilities

Respuesta :

Answer:

A)

Given that,

On each trial, the machine outputs a ball with one of the digits 0 through 9 on it.

To find the probability of getting 6.

In each trail the probability of getting 6 is,

[tex]p=\frac{1}{10}[/tex]

Let X be the event of getting 6.

we get

[tex]P(X=6)=nC_r(p)^r(q)^{n-r}[/tex]

we get,

[tex]q=1-p=1-\frac{1}{10}=\frac{9}{10}[/tex]

where n=50 and r=8

n is the total number of trials

r is the sucess trail.

Substitute the values we get,

[tex]P(X=6)=50C_8(\frac{1}{10})^8(\frac{9}{10})^{50-8}[/tex][tex]=50C_8(\frac{1}{10})^8(\frac{9}{10})^{42}[/tex]

Hence the required probability is,

[tex]=50C_8(\frac{1}{10})^8(\frac{9}{10})^{42}[/tex]

On simplifying we get,

[tex]=0.06487\approx0.06[/tex]

Answer is: 0.06

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