MHT CET · Maths · Probability
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
- A \(\frac{8}{19} \times \frac{7}{18}\)
- B \(\frac{8}{19}\)
- C \(\frac{8}{19} \times \frac{7}{19}\)
- D \(\frac{7}{18}\)
Answer & Solution
Correct Answer
(D) \(\frac{7}{18}\)
Step-by-step Solution
Detailed explanation
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 \(=\frac{7}{18}\).
\(\therefore\) The probability that second guest will get a room with prime number \(=\frac{7}{18}\).
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