Question

7 balls are thrown into 4 bags numbered serially 1, 2, 3 & 4. Then the probability that none of them found in bag number 2 is

• A. $\frac{3}{4}$
• B. $\frac{1}{4}$
• C. $(\frac{3}{4}{)}^7$
• D. $1-(\frac{1}{4}{)}^7$

Answer 1

The correct option is C $(\frac{3}{4}{)}^7$

No. of ways in which $7$ balls can be put in bag $1,3,4=3^7$ (each ball can be assigned one bag)
$P=(3\ast 3\ast 3\ast 3\ast 3\ast 3\ast 3)/(4\ast 4\ast 4\ast 4\ast 4\ast 4\ast 4)$
$\Rightarrow P=(\frac{3}{4}{)}^7$