Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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Mark the Correct Alternative in the Following Question: the Probability that a Person is Not a Swimmer is 0.3. the Probability that Out of 5 Persons 4 Are Swimmers is - Mathematics

Question

Mark the correct alternative in the following question:
The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is

Options
  • \[^{5}{}{C}_4 \left( 0 . 7 \right)^4 \left( 0 . 3 \right)\]

  • \[^{5}{}{C}_1 \left( 0 . 7 \right) \left( 0 . 3 \right)^4\]

  • \[^{5}{}{C}_4 \left( 0 . 7 \right) \left( 0 . 3 \right)^4\]

  • \[\left( 0 . 7 \right)^4 \left( 0 . 3 \right)\]

Solution

\[\text{ We have,}  \]

\[q = \text{ probability that a person is not a swimmer = 0 . 3 and } \]

\[\text{ p = probability that a person is a swimmer}  = 1 - q = 1 - 0 . 3 = 0 . 7\]

\[\text{ Let X denote a success that a person selected is a swimmer . Then, } \]

\[\text{ X follows the binomial distribution with parameters n = 5 and } p = 0 . 7\]

\[ \therefore P\left( X = r \right) = ^{5}{}{C}_r p^r q^\left( 5 - r \right) = ^{5}{}{C}_r \left( 0 . 7 \right)^r \left( 0 . 3 \right)^\left( 5 - r \right) \]

\[\text{ Now,}  \]

\[\text{ The required probability } = P\left( X = 4 \right) = ^{5}{}{C}_4 \left( 0 . 7 \right)^4 \left( 0 . 3 \right)^\left( 5 - 4 \right) =^{5}{}{C}_4 \left( 0 . 7 \right)^4 \left( 0 . 3 \right)\]

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 12 (Set of 2 Volume) (2018 (Latest))
Chapter 33: Binomial Distribution
MCQ | Q: 28 | Page no. 30
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Mark the Correct Alternative in the Following Question: the Probability that a Person is Not a Swimmer is 0.3. the Probability that Out of 5 Persons 4 Are Swimmers is Concept: Bernoulli Trials and Binomial Distribution.
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