The probability of a student qualifying for I | vedclass

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(C) Let $A$ be the event of qualifying for $IITJEE$ and $B$ be the event of qualifying for $EAMCET$. Given: $P(A) = \frac{1}{5}$ and $P(B) = \frac{3}{

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$\frac{17}{25}$

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(C) Let $A$ be the event of qualifying for $IITJEE$ and $B$ be the event of qualifying for $EAMCET$. Given: $P(A) = \frac{1}{5}$ and $P(B) = \frac{3}{5}$. Assuming the events are independent,the probability of qualifying for at least one test is given by $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. Since the events are independent,$P(A \cap B) = P(A) \cdot P(B) = \frac{1}{5} \cdot \frac{3}{5} = \frac{3}{25}$. Therefore,$P(A \cup B) = \frac{1}{5} + \frac{3}{5} - \frac{3}{25}$. Converting to a common denominator of $25$: $P(A \cup B) = \frac{5}{25} + \frac{15}{25} - \frac{3}{25} = \frac{17}{25}$.

The probability of a student qualifying for $IITJEE$ and $EAMCET$ are $\frac{1}{5}$ and $\frac{3}{5}$ respectively. The probability that the student qualifies for at least one of these tests is:

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