QJEEM22Maca5f: JEE Main 2022 Mathematics - Class 12 JEEM22Maca5f Solution: A six faced die is biased such that 3 × P ( a prime number ) =…

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QJEEM22Maca5f: JEE Main 2022 Mathematics - Class 12 JEEM22Maca5f Solution: A six faced die is biased such that 3 × P ( a prime number ) =…

A six faced die is biased such that

$3 \times P ($ a prime number $) = 6 \times P ($ a composite number $) = 2 \times P (1)$ .

Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of X is :

Multiple Choice Options

A 311
B 511
C 711
D 811

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Accepted Answer

Let P(a prime number) = $α$

P(a composite number) = $β$

and P(1) = $γ$

$∵$ $3 α = 6 β = 2 γ = k$ (say)

and $3 α + 2 β + γ = 1$

$\Rightarrow k + \frac{k}{3} + \frac{k}{2} = 1 \Rightarrow k = \frac{6}{11}$

Mean = np where n = 2

and p = probability of getting perfect square

$= P (1) + P (4) = \frac{k}{2} + \frac{k}{6} = \frac{4}{11}$

So, mean $= 2 . (\frac{4}{11}) = \frac{8}{11}$

QJEEM22Maca5f: JEE Main 2022 Mathematics - Class 12 JEEM22Maca5f Solution: A six faced die is biased such that 3 × P ( a prime number ) =…

Multiple Choice Options

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