Question

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

Answer 1

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,

`p=(1)/(10)`

Let X be the event of getting 6.

we get

`P(X=6)=nC_r(p)^r(q)^(n-r)`

we get,

`q=1-p=1-(1)/(10)=(9)/(10)`

where n=50 and r=8

n is the total number of trials

r is the sucess trail.

Substitute the values we get,

`P(X=6)=50C_8((1)/(10))^8((9)/(10))^(50-8)`
`=50C_8((1)/(10))^8((9)/(10))^(42)`

Hence the required probability is,

`=50C_8((1)/(10))^8((9)/(10))^(42)`

On simplifying we get,

`=0.06487\approx0.06`

Answer is: 0.06