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Mathematics - Probability Question with Solution | TestHub

MathematicsProbabilityTotal probability/Bay's TheoremEasy2 minPYQ_2019

MathematicsEasysingle choice

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least $90 %$ is:

Options:

Answer:

Solution:

Let a fair coin is tossed $n$ times, then
$P (at least one head) = 1 - P (all tails)$
$= 1 - {(\frac{1}{2})}^{n} > \frac{90}{100}$ (given)
$\Rightarrow {(\frac{1}{2})}^{n} < 1 - \frac{90}{100} = \frac{1}{10}$
$\Rightarrow 2^{n} > 10$
$\Rightarrow n \geq 4$

Stream:JEESubject:MathematicsTopic:ProbabilitySubtopic:Total probability/Bay's Theorem

⏱ 2mℹ️ Source: PYQ_2019

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