One out of every 119 tax returns that a tax auditor examines requires an audit. Find the probability that (a) the first return requiring an audit is the 25th return the tax auditor examines, (b) the first return requiring an audit is the first or second return the tax auditor examines, and (c) none of the first five returns the tax auditor examines require an audit.

A) 0.00686

B) 0.01673

C) 0.99587

Step-by-step explanation:

For this question, we are interested in the first success and we will Thus make use of geometric probability distribution.

It goes by the formula;

P(x) = [(1 - p)^(x - 1)]p

We are told that One out of every 119 tax returns that a tax auditor examines requires an audit.

Thus; p = 1/119 = 0.0084

A) Probability that the first return requiring an audit is the 25th return the tax auditor examines is given by;

P(25) = [(1 - 0.0084)^(25 - 1)]0.0084

P(25) = 0.00686

B) Probability the first requiring an audit is the first or second return the tax auditor examines, is;

P(1 or 2) = P(1) + P(2)

P(1) = [(1 - 0.0084)^(1 - 1)]0.0084

P(1) = 0.0084

P(2) = [(1 - 0.0084)^(2 - 1)]0.0084

P(2) = 0.00833

Thus;

P(1 or 2) = 0.0084 + 0.00833

P(1 or 2) = 0.01673

C) Probability that none of the first five returns the tax auditor examines require an audit is given by;

P(X > 5) = 1 - P(X ≤ 5)

Now,

P(X ≤ 5) is expressed as;

P(X ≤ 5) = P(1) + P(2) + P(3) + P(4) + P(5)

We know P(1) & P(2) already. Let's find P(3), P(4) and P(5)

P(3) = [(1 - 0.0084)^(3 - 1)]0.0084

P(3) = 0.00826

P(4) = [(1 - 0.0084)^(4 - 1)]0.0084

P(4) = 0.00819

P(5) = [(1 - 0.0084)^(5 - 1)]0.0084

P(5) = 0.00812

P(X ≤ 5) = 0.0084 + 0.00833 + 0.00826 + 0.00819 + 0.00812

P(X ≤ 5) = 0.00413

P(X > 5) = 1 - 0.00413

P(X > 5) = 0.99587

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?

these sign is used to tell weather the number is greater or less than the number   <   or >     but this sign means its equal =    

hope this you and

step-by-step explanation: