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Mathematics - Probability Question with Solution | TestHub

MathematicsProbabilityRandom Variable and its Probability DistributionMedium2 minQB

MathematicsMediumnumerical

A bacterium dies, splits into two, or splits into three with probabilities 1/4, 1/2, 1/4. Its probability of surviving indefinitely is $(m - 13) / n$ , where $m, n \in N$ . Find $m / n$ .

Answer:

2.50

Solution:

If $q$ is the extinction probability, then $q = 1/4 + q^{2} /2 + q^{3} /4$ . The relevant root is $(13 - 3) /2$ , so the survival probability is $(5 - 13) /2$ . Therefore $m / n = 5/2 = 2.50$ .

Stream:JEESubject:MathematicsTopic:ProbabilitySubtopic:Random Variable and its Probability Distribution

⏱ 2mℹ️ Source: QB

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