Question

एक बक्सा जिसमें 5 सफेद तथा 4 काली गेंदे हैं, से 3 गेंदे निकाली जाती है उन तीनों के सफेद होने की क्या संभावना है​

Answer 1

Given:

A box contains 5 white balls and 4 black balls

To find:

The probability of getting 3 white balls in a draw of balls from a box containing 5 white and 4 black balls

Solution:

No. of white balls in the box = 5  

No. of black balls in the box = 4

∴ Total no. of balls in the box = 5 + 4 = 9

We know that,

$\boxed{\boxed{\bold{Probability = \frac{No. \:of \:favorable\:outcomes}{Total\: no.\: of\: outcomes } }}}$

 

We will find the probability of getting 3 white balls in a draw of balls from the box, both with replacement and without replacement :

Case (1): When 3 balls are drawn from the box with replacement

Therefore,

The probability of getting 3 white balls in a draw of balls from a box containing 5 white and 4 black balls is,

=   $\frac{5}{9} \times \frac{5}{9} \times \frac{5}{9}$

=   $\underline {\bold{\frac{125}{729} }}$

Case (2): When 3 balls are drawn from the box without replacement

Therefore,

The probability of getting 3 white balls in a draw of balls from a box containing 5 white and 4 black balls is,

=   $\frac{5}{9} \times \frac{4}{8} \times \frac{3}{7}$

=   $\frac{60}{504}$

dividing both the numerator and denominator by 12 we get

=   $\underline{\bold{\frac{5}{42}}}$

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