Question

If 12 identical balls are to be placed in 3 different boxes, then the probability that a particular box contains exactly 3 balls, is?

• A. $\frac{55}{3}(\frac{2}{3}{)}^{11}$
• B. $55(\frac{2}{3}{)}^{10}$
• C. $220(\frac{1}{3}{)}^{12}$
• D. $22(\frac{1}{3}{)}^{11}$

Answer 1

The correct option is A $\frac{55}{3}(\frac{2}{3}{)}^{11}$

We have mentioned that boxes are different and one particular box has 3 balls.
Consider the random experiment of choosing a particular box at random and putting a ball into the chosen box.
Repeat the experiment 12 times. The 12 trials are Bernoulli trials with $p=\frac{1}{3},q=\frac{2}{3}andn=12$
The required probability is the probability of 3 successes in 12 trials.
$P(X=3)=\frac{{}^{12}{C}_3\times 2^9}{3^{12}}=\frac{55}{3}(\frac{2}{3}{)}^{11}$