Question

एक बक्सा जिसमें 5 सफेद तथा चार काली कहते हैं से 3 गेंदे निकाली जाती हैं 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,

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

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,

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

= $\frac{5^3}{9^3}$

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

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,

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

= $\frac{5}{3} \:\times\:\frac{1}{2}\:\times\: \frac{1}{7}$

= $\underline{\bold{\frac{5}{42} }}$

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