Probability of All Balls Being White Given Two Are White – Probability Theory

probability

A bag contains $4$ balls .Two balls are drawn at random and are found to be white.

What is the probability that all the four balls in the bag are white?.

The options are
$\large\frac{1}{5}\space ;\frac{2}{5} ;\frac{3}{5} ;\frac{4}{5}$

My work:
It's given that two balls are white.So the rest of the balls could be

  1. all white
  2. One of them white
  3. none of them white

So among the three above possibilities only one satisfies our conditions so the probability is $\frac{1}{3}$.But it not even the options given. What's wrong with my work?

Best Answer

This question cannot be answered as it is stated. You need to make some assumptions about the probabilities of the balls in the bag. How were the 4 balls chosen? Randomly between white and non-white? Randomly between white and 10 other colors?

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