Two slips from a pack of 150 cards numbered 1 to 150 are drawn at random. What is the probability that at most one of the two slips drawn contains multiple of 7 and 9?

Option 1 : 11174/11175

**Given:**

Two slips from a pack of 150 cards numbered 1 to 150 are drawn at random.

**Concepts used:**

Probability that number on at most one slip is a multiple of 7 and 9 = P (number on none of the slips is multiple of 7 and 9) + P (number on one slip is multiple of 7 and 9)

**Calculation:**

There are total of 150 slips with slips numbered from 1 to 150.

⇒ Number of slips having number as multiple of both 7 and 9 = 2 (63, 126)

Probability that number on at most one slip is a multiple of 7 and 9 = P (number on none of the slips is multiple of 7 and 9) + P (number on one slip is multiple of 7 and 9)

Two slips are drawn at random.

⇒ Probability that number on at most one slip is a multiple of 7 and 9 = {(148/150) × (147/149)} + {2 × (2/150) × (148/149)} = (3626/3725) + (296/11175) = 11174/11175

**∴ Probability that number on at most one slip is a multiple of 7 and 9 is 11174/11175.**