Answer to Question #298697 in Statistics and Probability for Sannie

Question

A BASKET CONTAINS 5 WHITE BALL (W) AND 5 BLACK BALL (B). WHAT IS THE POSSIBLE RESULT IF YOU DRAW 3 BALLS IN RANDOM FROM THE BASKET. LET X BE THE RANDOM VARIABLE REPRESENTING THE NUMBER OF BALCK BALL THAT OCCUR.

Answer 1

$P(X=0)=\frac{5}{10}*\frac{4}{9}*\frac{3}{8}=\frac{1}{12}.$

$P(X=1)=\frac{5}{10}*\frac{5}{9}*\frac{4}{8}*C_3^1=\frac{5}{12}.$

$P(X=2)=\frac{5}{10}*\frac{4}{9}*\frac{5}{8}*C_3^2=\frac{5}{12}.$

$P(X=3)=\frac{5}{10}*\frac{4}{9}*\frac{3}{8}=\frac{1}{12}.$