Question 1191263
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Write the probability distribution of a random variable R representing the number 
of red balls when 3 balls are drawn in succession without replacement from a jar 
containing 4 reds and 5 blue balls.
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There are 4 possible values for  R :   they are  0,  1,  2  and  3.


Notice that the total balls is   4 + 5 = 9.



<pre>
R = 0 :  P(0) = {{{(C[5]^3*C[4]^0)/C[9]^3}}} = {{{(10*1)/84}}} = {{{10/84}}} = {{{5/42}}}.


R = 1 :  P(1) = {{{(C[5]^2*C[4]^1)/C[9]^3}}} = {{{10*4)/84}}} = {{{40/84}}} = {{{20/42}}}.


R = 2 :  P(2) = {{{(C[5]^1*C[4]^2)/C[9]^3}}} = {{{5*6)/84}}} = {{{30/84}}} = {{{15/42}}}.


R = 3 :  P(3) = {{{(C[5]^0*C[4]^3)/C[9]^3}}} = {{{1*4)/84}}} = {{{4/84}}} = {{{2/42}}}.



I intentionally left these fractions in this form, not fully reduced.


You can easily check that the sum of all probabilities equals to 1.
</pre>

Solved.