Mathematics - Probability Question with Solution | TestHub

MathematicsProbabilityTotal probability/Bay's TheoremEasy2 minPYQ_2021

MathematicsEasynumerical

A fair coin is tossed $n -$ times such that the probability of getting at least one head is at least $0.9 .$ Then the minimum value of $n$ is _______.

Answer:

4.00

Solution:

When a coin is tossed, then probability of head, $P (Head) = P (Tail) = \frac{1}{2}$

Therefore, $1 - P$ (All tail) $\geq 0.9$

$\Rightarrow 1 - {(\frac{1}{2})}^{n} \geq 0.9$

$\Rightarrow {(\frac{1}{2})}^{n} \leq \frac{1}{10}$

$\Rightarrow n_{\min} = 4 .$

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

⏱ 2mℹ️ Source: PYQ_2021

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