(D) The prime numbers between $1$ and $19$ are $2, 3, 5, 7, 11, 13, 17, 19$. There are $8$ such numbers.Since the first guest is given a room with a p

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(D) The prime numbers between $1$ and $19$ are $2, 3, 5, 7, 11, 13, 17, 19$. There are $8$ such numbers.Since the first guest is given a room with a prime number,there are $8 - 1 = 7$ prime-numbered rooms remaining.The total number of rooms remaining for the second guest is $19 - 1 = 18$.Therefore,the probability that the second guest is given a room with a prime number is $\frac{7}{18}$.

Class 12 Mathematics Differential Equations Homogeneous differential equations

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Rooms in a hotel are numbered from $1$ to $19$. Rooms are allocated at random as guests arrive. The first guest to arrive is given a room which is a prime number. The probability that the second guest to arrive is given a room which is a prime number is

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A
$\frac{8}{19} \times \frac{7}{18}$
B
$\frac{8}{19}$
C
$\frac{8}{19} \times \frac{7}{19}$
D
$\frac{7}{18}$

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Rooms in a hotel are numbered from $1$ to $19$. Rooms are allocated at random as guests arrive. The first guest to arrive is given a room which is a prime number. The probability that the second guest to arrive is given a room which is a prime number is

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