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

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MCQ

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

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

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

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

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

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#### Solution

$\text{ We have,}$

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

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

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

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

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

$\text{ Now,}$

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

Concept: Bernoulli Trials and Binomial Distribution
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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 33 Binomial Distribution
MCQ | Q 28 | Page 30

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