Question 329387
Each soccer player gets 4 jerseys red, yellow, white and green.  A player randomly draws 2 jerseys each from the bag.  The first jersey is not placed back in the bag.

A.  What is the probability of first drawing a white and then a green jersey?
<pre><b>
We (1) draw a white AND (2) then draw a green.

We start with this set of 16

R, R, R, R, Y, Y, Y, Y, W, W, W, W, G, G, G, G

(1) We can draw a white any of 4 ways out of 16.  That's a probability of {{{4/16}}},  which reduces to {{{1/4}}},

<font size = 7>AND</font> then that leaves this set of 15:

R, R, R, R, Y, Y, Y, Y, W, W, W, G, G, G, G

(2) We can then draw a green one any of 4 ways out of 15.  That's a probability of {{{4/15}}}.

That's all we wanted to do.  Since the big word between 1 and 2 is <font size = 7>AND</font>, we multiply those probabilities:

Answer 

{{{1/4}}}{{{""*""}}}{{{4/15}}}

{{{1/cross(4)}}}{{{""*""}}}{{{cross(4)/15}}}

{{{1/15}}}

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</pre></b>    
B. What is the probability of drawing a red and yellow jersey in any order?
<pre><b>
  What is the probability of first drawing a white and then a green jersey?

We (1) draw a red AND (2) then draw a yellow OR we (3) draw a yellow AND (4) then draw a red.

We start with this set of 16

R, R, R, R, Y, Y, Y, Y, W, W, W, W, G, G, G, G

(1) We can draw a red any of 4 ways out of 16.  That's a probability of {{{4/16}}},  which reduces to {{{1/4}}},

<font size = 7>AND</font> then that leaves this set of 15:

R, R, R, Y, Y, Y, Y, W, W, W, W, G, G, G, G

(2) We can then draw a yellow any of 4 ways out of 15.  That's a probability of {{{4/15}}}.

<font size = 7>OR</font>

We start with this set of 16

R, R, R, R, Y, Y, Y, Y, W, W, W, W, G, G, G, G

(1) We can draw a yellow any of 4 ways out of 16.  That's a probability of {{{4/16}}},  which reduces to {{{1/4}}},

<font size = 7>AND</font> then that leaves this set of 15:

R, R, R, R, Y, Y, Y, W, W, W, W, G, G, G, G

(2) We can then draw a red one any of 4 ways out of 15.  That's a probability of {{{4/15}}}.

 Red {{{1/4}}} AND yellow {{{4/15}}}OR yellow {{{1/4}}} AND red {{{4/15}}}  

AND means to multiply and OR means to add:

{{{1/4}}}{{{x}}}{{{4/15}}}{{{""+""}}}{{{1/4}}}{{{x}}}{{{4/15}}}

{{{1/cross(4)}}}{{{x}}}{{{cross(4)/15}}}{{{""+""}}}{{{1/cross(4)}}}{{{x}}}{{{cross(4)/15}}}

Answer 

{{{1/4}}}{{{""*""}}}{{{4/15}}}{{{""+""}}}{{{1/4}}}{{{""*""}}}{{{4/15}}}

{{{1/cross(4)}}}{{{""*""}}}{{{cross(4)/15}}}{{{""+""}}}{{{1/cross(4)}}}{{{""*""}}}{{{cross(4)/15}}}

{{{1/15}}}{{{""+""}}}{{{1/15}}}{{{""=""}}}{{{2/15}}}

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</pre></b>
C.  What is the probablity of not drawing a red jersey?
<pre><b>
We (1) draw a non-red AND (2) then draw another non-red.

We start with this set of 16

R, R, R, R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R

(1) We can draw a non-red any of 12 ways out of 16.  That's a probability of {{{12/16}}},  which reduces to {{{3/4}}},

<font size = 7>AND</font> then that leaves this set of 15:

R, R, R, R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R 

(2) We can then draw a non-red any of 11 ways out of 15.  That's a probability of {{{11/15}}}.

That's all we wanted to do.  Since the big word between 1 and 2 is <font size = 7>AND</font>, we multiply those probabilities:

Answer 

{{{3/4}}}{{{""*""}}}{{{11/15}}}

{{{cross(3)/4}}}{{{""*""}}}{{{11/(""[5]cross(15))}}}

{{{11/20}}}

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</pre></b>
D. What is the probablity of having a white or red jersey after the second draw?
<pre><b>
This requires finding the probability of the complenment event, and
then subtracting from 1

COMPLEMENT EVENT:

(1) Drawing a non-white-non-red AND (2) then drawing another non-white-non-red 

We start with this set of 16

R, R, R, R, W, W, W, W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W

(1) We can draw a non-red-non-white any of 8 ways out of 16.  That's a probability of {{{8/16}}},  which reduces to {{{1/2}}},

<font size = 7>AND</font> then that leaves this set of 15:

R, R, R, R, W, W, W, W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W

(2) We can draw a non-red-non-white any of 7 ways out of 15.  That's a probability of {{{7/15}}}.

Answer to COMPLEMENT event:

{{{1/2}}}{{{""*""}}}{{{7/15}}}

{{{7/30}}}

Answer to DESIRED event:

{{{1}}}{{{""-""}}}{{{7/30}}}

{{{30/30}}}{{{""-""}}}{{{7/30}}}

{{{23/30}}}

Edwin</pre>