Answer to Question #209856 in Statistics and Probability for niks

Question #209856

Two balls are drawn in succession without replacement from an urn containing 4 red balls and 3 black balls. Find the probability distribution of the number of black balls. 


1
Expert's answer
2021-06-23T17:51:18-0400

Number of Red balls =4=4  

Number of Black balls =3=3

Total number of balls =4+3=7=4+3=7

Given: two balls are drawn in succession without replacement. 

Let X=X= the number of black balls: X=0,1,2.X=0,1,2.


P(X=0)=(42)(30)(72)=621=27P(X=0)=\dfrac{\dbinom{4}{2}\dbinom{3}{0}}{\dbinom{7}{2}}=\dfrac{6}{21}=\dfrac{2}{7}


P(X=1)=(41)(31)(72)=4(3)21=47P(X=1)=\dfrac{\dbinom{4}{1}\dbinom{3}{1}}{\dbinom{7}{2}}=\dfrac{4(3)}{21}=\dfrac{4}{7}

P(X=2)=(40)(32)(72)=321=17P(X=2)=\dfrac{\dbinom{4}{0}\dbinom{3}{2}}{\dbinom{7}{2}}=\dfrac{3}{21}=\dfrac{1}{7}

x012p(x)2/74/71/7\def\arraystretch{1.5} \begin{array}{c:c} x & 0 & 1 & 2 \\ \hline p(x) & 2/7 & 4/7 & 1/7 \\ \end{array}

E[X]=0(27)+1(47)+2(17)=67E[X]=0(\dfrac{2}{7})+1(\dfrac{4}{7})+2(\dfrac{1}{7})=\dfrac{6}{7}



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment