A positive integer n not exceeding $$100$$ is chosen at random in such a way that, p is the probability of choosing n≤$$50$$ and $$3p$$ is the probability of choosing n$$50$$. If λ is probability that a perfect square is chosen, then the value of [$$100$$λ] $$($$[.] → $$GIF)$$

Question

A positive integer n not exceeding $$100$$ is chosen at random in such a way that, p is the  probability of choosing n≤$$50$$ and $$3p$$ is the probability of choosing n>$$50$$. If λ is  probability that a perfect square is chosen, then the value of [$$100$$λ] $$($$[.] → $$GIF)$$

Infinity Learn · Accepted Answer

Since the probability is p for choosing n≤$$50$$ and $$3p$$ for choosing n≥$$50$$ , then $$50p+50(3p)=1$$⇒$$p=0.05$$⇒$$50p+150p=1$$⇒$$200p=1$$⇒$$p=1200=0.05$$∴ Required probability is $$7p+3(3p)=16p=0.08$$∴   $$100$$λ$$=8$$

Theorems of probability

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$A positive integer n not exceeding 100 is chosen at random in such a way that, p is the$
$probability of choosing n \leq 50 and 3 p is the probability of choosing n > 50 . If λ is$
$probability that a perfect square is chosen, then the value of [100 λ] ([.] \to GIF)$

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Theorems of probability

Remember concepts with our Masterclasses.

A positive integer n not exceeding 100 is chosen at random in such a way that, p is the probability of choosing n≤50 and 3p is the probability of choosing n>50. If λ is probability that a perfect square is chosen, then the value of [100λ] ([.] → GIF)

Since the probability is p for choosing n≤50 and 3p for choosing n≥50 , then 50p+50(3p)=1⇒p=0.05⇒50p+150p=1⇒200p=1⇒p=1200=0.05∴ Required probability is 7p+3(3p)=16p=0.08∴ 100λ=8

Ready to Test Your Skills?

free study material

$A positive integer n not exceeding 100 is chosen at random in such a way that, p is the$
$probability of choosing n \leq 50 and 3 p is the probability of choosing n > 50 . If λ is$
$probability that a perfect square is chosen, then the value of [100 λ] ([.] \to GIF)$