Answer:
The slope is (DNE), undefined.
Step-by-step explanation:
Conditional probability is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B), or sometimes
.
The conditional probability of event A happening, given that event B has happened, written as P(A|B) is given by
In the question, we were told that there are three randomly selected coins which can be a nickel, a dime or a quarter.
The probability of selecting one coin is
Part A:
To find <span>the probability that all three coins are quarters if the first two envelopes Jeanne opens each contain a quarter, let the event that all three coins are quarters be A and the event that the first two envelopes Jeanne opens each contain a quarter be B.
P(A) means that the first envelope contains a quarter AND the second envelope contains a quarter AND the third envelope contains a quarter.
Thus
</span><span>P(B) means that the first envelope contains a quarter AND the
second envelope contains a quarter
</span><span>Thus
Therefore,
Part B:
</span>To find the probability that all three coins are different if the first envelope Jeanne opens contains a dime<span>, let the event that all three coins are different be C and the event that the first envelope Jeanne opens contains a dime be D.
</span><span>
</span><span>
</span><span>
Therefore,
</span>
First of all, we compute the points of interest, i.e. the points where the curve cuts the x axis: since the expression is already factored, we have
Which means that the roots are
Next, we can expand the function definition:
In this form, it is much easier to compute the derivative:
If we evaluate the derivative in the points of interest, we have
This means that we are looking for the equations of three lines, of which we know a point and the slope. The equation
is what we need. The three lines are:
This is the tangent at x = -2
This is the tangent at x = 0
This is the tangent at x = 1
Parallel means it has the same slope.
Slope in thisproblem is -5/4.
This means the slope of the parallel line is also -5/4.
Perpendicular is the reciprical of the slope.
Flip the slope and make it +/-.
The slope would be 4/5.