Question:
A bag contains $6$ red, $4$ blue and $2$ yellow balls. Three balls are drawn one by one with replacement. Find the probability of getting exactly one red ball.
A bag contains $6$ red, $4$ blue and $2$ yellow balls. Three balls are drawn one by one with replacement. Find the probability of getting exactly one red ball.
Updated On: Jul 5, 2022
- $\frac{1}{4}$
- $\frac{3}{8}$
- $\frac{3}{4}$
- $\frac{1}{2}$
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The Correct Option is B
Solution and Explanation
Let $A$ be the event that ball drawn is red, then
$p= \frac{6}{12} = \frac{1}{2}$,
$q=1-\frac{1}{2}=\frac{1}{2}$ and $n = 3$
$\therefore$ Probability of drawing exactly $1$ red ball in $3$ trials
$= \,^{3}C_{1}pq^{2} = \,^{3}C_{1}\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)^{2} = \frac{3}{8}$.
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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:
- Semiconductor acts like an insulator at Zero Kelvin. On increasing the temperature, it works as a conductor.
- Due to their exceptional electrical properties, semiconductors can be modified by doping to make semiconductor devices suitable for energy conversion, switches, and amplifiers.
- Lesser power losses.
Uses of Semiconductor:
- Semiconductors are widely used in manufacturing electronics devices like transistors, diodes, sensors, integrated circuits.
- Semiconductors are widely used in all electronic devices, like mobile phones, digital cameras, communication devices, trains, ATMs, etc.