Four bad apples are accidently mixed with sixteen good apples. Let X denote the number of bad apples in a random draw of two apples. Then

A. $P(X=0)=\frac{12}{19}$

B. $E(X)=\frac{3}{5}$

C. Standard Deviation of $X=\frac{12}{5\sqrt{19}}$

D. $P(X+2)=\frac{32}{95}$

E. $Var(X)=\frac{144}{475}$

Choose the correct answer from the options given below :

Only A

The correct answer is Option (3) → Only A

Ways to Choose 2 good apples,

Ways = ${^{16}C}_2=120$

Ways to Choose any 2 apples,

${^{20}C}_2=190$

$∴P(X=0)=\frac{120}{190}=\frac{12}{19}$ ($X=0$; Both apples are good)