Rooms in a hotel are numbered from 1 to 19 . Rooms are allocated at random as guests arrive. The first guest…
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
$\frac{8}{19} \times \frac{7}{18}$
$\frac{8}{19}$
$\frac{8}{19} \times \frac{7}{19}$
$\frac{7}{18}$
Solution
Prime numbers from 1 to 19 are $2,3,5,7,11,13,17,19$ i.e. 8 such numbers. The room with prime number is given to the first guest.
$\therefore$ The probability that second guest will get a room with prime number $=\frac{7}{18}$.