Question:
A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals:
A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals:
Updated On: Jul 5, 2022
- $\frac{1}{32}$
- $\frac{1}{2}$
- $\frac{3}{2}$
- $\frac{1}{5}$
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The Correct Option is B
Solution and Explanation
Let A be the event of getting tail in first four trial and B be the event of getting head in fifth trial.
$\therefore P\left(A\right) = \left(\frac{1}{2}\right)^{4} P\left(B\right) = \left(\frac{1}{2}\right)^{5} $
$\because P\left(A \cap B\right) = P\left(A\right).P\left(B\right) = \left(\frac{1}{2}\right)^{5} $
$\because$ A and B are independent events
$\therefore$ Probability of head appearing on fifth toss equal.
$P\left(\frac{B}{A}\right) = \frac{P\left(A\cap B\right)}{P\left(A\right)\times P\left(B\right)} = \frac{\left(\frac{1}{2}\right)^{5}}{\left(\frac{1}{2}\right)^{4}} = \left(\frac{1}{2}\right)$
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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.