Probability · JEE Main previous year questions

2005 2 questions

1. Q362005 · 28 Apr 2005 · Shift 1

   Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is :

   1. A.$\frac{2}{9}$
   2. B.$\frac{1}{9}$
   3. C.$\frac{8}{9}$
   4. D.$\frac{7}{9}$
   Show answer

   Answer: B

2. Q382005 · 28 Apr 2005 · Shift 1

   Let $A$ and $B$ two events such that $P\left(\overline{A\cup B}\right)=\frac{1}{6}$, $P(A\cap B)=\frac{1}{4}$ and $P\left(\overline{A}\right)=\frac{1}{4}$, where $\overline{A}$ stands for complement of event $A$. Then events $A$ and $B$ are :

   1. A.equally likely and mutually exclusive
   2. B.equally likely but not independent
   3. C.independent but not equally likely
   4. D.mutually exclusive and independent
   Show answer

   Answer: C