Question

Rooms in a hotel are numbered from 1 to 19. Rooms are allocated at random as guests arrive. tThe probability that the first guest to arrive is given a room which is a prime number (1 is Not a prime number) is 8/19

The question is
What is the probability that the second guest to arrive is given a room which is a prime number?

Answer 1

Rooms in a hotel are numbered from 1 to 19.  probability that the second guest to arrive is given a room which is a prime number = 8/19

Step-by-step explanation:

1 to 19 Prime numbers

2  , 3 , 5 , 7 , 11 , 13 , 17 , 19   - 8 Prime Numbers

11 - non Prime numbers

total Numbers = 19

The probability that the first guest to arrive is given a room which is a prime number = 8/19  

probability that the second guest to arrive is given a room which is a prime number (Not specified any thing about 1st guest)

so there are two cases that 1st guest Prime number or Non-prime Numbers

Case 1 :  Guest 1 Get Prime Number

then Probability = (8/19)(7/18)

Case 2 : Guest 1 Get non - Prime Number

Then Probability = (11/19)( 8/18)

Total Probability =    (8/19)(7/18) + (11/19( 8/18)

= ( 56 + 88)/(19 * 18)

= 144/ ( 19 * 18)

= 8/19

probability that the second guest to arrive is given a room which is a prime number = (8/19)