Question:

A bag contains $12$ white pearls and $18$ black pearls. Two pearls are drawn in succession without replacement. Find the probability that the first pearl is white and the second is black.

Updated On: Jul 5, 2022
  • $\frac{32}{145}$
  • $\frac{28}{143}$
  • $\frac{36}{145}$
  • $\frac{36}{143}$
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The Correct Option is C

Solution and Explanation

Let $A$ and $B$ be the events of getting a white pearl in the first draw and a black pearl in the second draw. Now $P(A) = P$(getting a white pearl in the first draw) $=\frac{12}{30} = \frac{2}{5}$ When second pearl is drawn without replacement, the probability that the second pearl is black is the conditional probability of the event $B$ occurring when $A$ has already occurred. $\therefore P(B|A) = \frac{18}{29}$ By multiplication rule of probability, we have $P(A\cap B) = P(A).P(B|A)=\frac{2}{5} \times \frac{18}{29}$ $= \frac{36}{145}$
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Notes on Conditional Probability

Concepts Used:

Semiconductors

Semiconductors are a crystalline solid materials, whose electrical conductivity lies between a conductor and an insulator. Semiconductors are mainly used in the manufacturing of electronic devices like capacitors, transistors, diodes, Integrated circuits, etc.

Properties of Semiconductor:

  1. Semiconductor acts like an insulator at Zero Kelvin. On increasing the temperature, it works as a conductor.
  2. Due to their exceptional electrical properties, semiconductors can be modified by doping to make semiconductor devices suitable for energy conversion, switches, and amplifiers.
  3. Lesser power losses.

Uses of Semiconductor:

  1. Semiconductors are widely used in manufacturing electronics devices like transistors, diodes, sensors, integrated circuits.
  2. Semiconductors are widely used in all electronic devices, like mobile phones, digital cameras, communication devices, trains, ATMs, etc.