Suppose you have two urns with poker chips in them. Urn I contains two red chips and four white chips. Urn II contains three red chips and one white chip. You randomly select one chip from urn I and put it into urn II. Then you randomly select a chip from urn II.

(a) What is the probability that the chip you select from urn II is white?
b) Is selecting a white chip from urn I and selecting a white chip from urn II independent? Justify your answer numerically.

Multiple answers

Step-by-step explanation:

The original urns have:

We take one chip from the first urn, so we have:

The probability of take a red one is : (2 red from 6 chips(2/6=1/2))

For a white one is: (4 white from 6 chips(4/6=(2/3))

Then we put this chip into the second urn:

We have two possible cases:

If we select a chip from the urn two:

This problem is a dependent event because the final result depends of the first chip we got from the urn 1.

For the fist case we multiply :

x = = 26.66%   ( the probability of taking a white chip from the urn 1,  the probability of taking a white chip from urn two)

For the second case we multiply:

x = = .06%   ( the probability of taking a red chip from the urn 1,   the probability of taking a white chip from the urn two)

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204