Introduction to probability

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Question

$A bag contains 5 balls of unknown colors such that a ball is drawn at random from it and is found to be white.$
$The probability that bag contains only white balls is$

Moderate

Solution

$Let W_{i} (i = 1, 2, 3, 4, 5) denotes i white balls and (5 - i) denotes$
other coloured balls.
W denotes event of selecting white ball.
$\begin{aligned} P (\frac{W}{W_{i}}) = \frac{i}{5}, (i = 1, 2, 3, 4, 5) \\ P (W_{i}) = \frac{1}{5}, (i = 1, 2, 3, 4, 5) \end{aligned}$
Probability of occurrence of W given $W_{5}$ has occurred
$\begin{array}{l} P (\frac{W}{W_{5}}) = \frac{P (W_{5}) \cdot P (\frac{W}{W_{5}})}{\sum_{i = 1}^{5} P (W_{i}) P (\frac{W}{W_{i}})} \\ = \frac{\frac{1}{5} \times 1}{\frac{1}{5} (\frac{1}{5} + \frac{2}{5} + \frac{3}{5} + \frac{4}{5} + \frac{5}{5})} = \frac{1}{3} \\ Therefore, the correct answer is 0.33 \end{array}$ $(B a y e' s t h e o r e m)$

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Introduction to probability

Remember concepts with our Masterclasses.

A bag contains 5 balls of unknown colors such that a ball is drawn at random from it and is found to be white. The probability that bag contains only white balls is

Ready to Test Your Skills?

free study material

$A bag contains 5 balls of unknown colors such that a ball is drawn at random from it and is found to be white.$
$The probability that bag contains only white balls is$