Each of the two boxes P and Q contain 100 chi | vedclass

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Question

(A) Let $x$ be the number on the chit drawn from box $Q$ and $y$ be the number on the chit drawn from box $P$. Both $x$ and $y$ are integers such that

Vedclass · Accepted Answer

$0.1$

Vedclass · Answer

(A) Let $x$ be the number on the chit drawn from box $Q$ and $y$ be the number on the chit drawn from box $P$. Both $x$ and $y$ are integers such that $1 \leq x, y \leq 100$.We are given the condition that $y = x^2$.Since $y \leq 100$, we must have $x^2 \leq 100$, which implies $x \leq 10$.Thus, the possible pairs $(x, y)$ are $(1, 1), (2, 4), (3, 9), (4, 16), (5, 25), (6, 36), (7, 49), (8, 64), (9, 81), (10, 100)$.There are $10$ such favorable outcomes.The total number of possible outcomes when drawing one chit from each box is $100 	imes 100 = 10000$.The probability is given by $\frac{	ext{Number of favorable outcomes}}{	ext{Total number of outcomes}} = \frac{10}{10000} = \frac{1}{1000}$.Converting this to a percentage: $\frac{1}{1000} 	imes 100\% = 0.1\%$.

Each of the two boxes $P$ and $Q$ contain $100$ chits numbered from $1$ to $100$. If one chit is drawn at random from each box, then the probability that the number on the chit drawn from $P$ is the square of the number on the chit drawn from $Q$, is (in $\%$)

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