Question

Ten slips of paper labeled from 1 to 10 are placed in a hat. The first slip of paper is not replaced before selecting the second slip of paper. What is the probability of selecting a number less than 2 then a number greater than 7?

A) 3/100
B) 3/50
C) 1/15
D) 1/30

Answer 1

The probability of selecting a slip of paper with a number less than 2 and then a number greater than 7, without replacement, from ten slips labeled 1 to 10 is 1/30.

Step-by-step explanation:

The question involves calculating the probability of two events occurring in sequence without replacement. The probability of selecting a number less than 2 from ten slips labeled 1 to 10 is 1/10, as there is only one such number (the number 1). After this first event, there are now 9 slips remaining. The probability of then selecting a number greater than 7 is 3/9 or 1/3, as there are three such numbers (8, 9, and 10).

To find the overall probability of both events occurring, we multiply the probabilities of each individual event:

Probability of selecting a number less than 2 and then a number greater than 7 = (1/10) × (1/3) = 1/30.

Therefore, the correct answer is D) 1/30.