Question

A box contains $100$ round discs, $50$ square - shaped discs and $30$ triangular discs. All the discs are made up of iron and have an equal probability of getting attracted by a magnet. If a magnet which can attract only one disc in one pass and the disc is passed over them twice. What is the probability that both times a triangular disc is attracted? The disc attracted in one pass does not fall into box again, however each time a square shaped disc is kept into the box.

• (A) $\frac{29}{180}$
• (B) $\frac{29}{1074}$
• (C) $\frac{1}{36}$
• (D) $\frac{29}{1080}$

Answer 1

The Correct Option is D

Explanation:
Given:A box contains $100$ round discs, $50$ square-shaped discs and $30$ triangular discs.Probability $=\frac{\text{ Number of observation }}{\text{ Total number of observation }}$Total number of discs $=180$Total number of triangular discs $=30$The probability that in first pass a triangular disc is attracted $=\frac{30}{180}$ $=\frac{1}{6}$The first disc is kept aside and one square disc is kept inside.The probability that in second pass a triangular disc is attracted $=\frac{29}{180}$ Required Probability $=\frac{1}{6}\times \frac{29}{180}$$=\frac{29}{1080}$$\therefore$ Required Probability is $\frac{29}{1080}$Hence, the correct option is (D).