Multiple choice

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

  1. $\displaystyle \frac{3}{4}$
  2. $\displaystyle \frac{1}{4}$
  3. $(\displaystyle \frac{3}{4})^{7}$
  4. $1-(\displaystyle \frac{1}{4})^{7}$
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C Correct answer
Explanation

For each ball, the probability of not being in bag 2 is 3/4. Since there are 7 balls, the probability that none are in bag 2 is (3/4)^7.

AI explanation

The scenario describes independent trials for each of the 7 balls thrown, where each ball avoids bag 2 with a specific probability. For one ball, the probability of going into any of the other 3 bags is 3 out of 4, or 3/4. Because each throw is independent, the probability that all 7 balls avoid bag 2 is found by multiplying this rate for each throw. The final probability is (3/4) multiplied by itself 7 times, written as (3/4)^7.

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