Question

Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students and let
E : event that you both enter the same section and
F : event that you both enter the different section, then

• A. $P(E) + P(F) = 1 $
• B. E and F are equally likely and exhaustive.
• C. $P(E) > P(F)$
• D. $P(E) < P(F)$

Answer 1

Answer: (A), (C)

$ n(S)=\frac{100 !}{40 ! \cdot 60 !}$
$n(F)=\frac{98 !}{39 ! \cdot 59 !} \cdot 2 ! \text { (think!) } $
$P(F)=\frac{98 ! \cdot 2 !}{39 ! \cdot 59 !} \frac{40 ! \cdot 60 !}{100 !}=\frac{2 \cdot 40 \cdot 60}{100 \cdot 99}=\frac{48}{99}=\frac{16}{33}$
$P(E)=\frac{16}{33} ; P(E)=\frac{17}{33} \Rightarrow(A) /(C)$ are correct.