Final answer:
The probability of selecting a slip with a number less than 2 and then a number greater than 7, without replacement, is 1/30, or approximately 3.33%. The options provided do not match this calculation.
Step-by-step explanation:
To calculate the probability of selecting a number less than 2 (which can only be 1 in this case) and then a number greater than 7 (which can be the numbers 8, 9, or 10), we need to consider that there are 10 slips and that events happen in succession without replacement.
First, we'll determine the probability of selecting a number less than 2. Since there is only one number (1) that satisfies this condition, we have:
- P(selecting a number less than 2) = 1/10
Next, assuming a number less than 2 (the number 1) has already been selected and not replaced, we now have 9 slips remaining. Among these 9 slips, there are 3 numbers that are greater than 7 (8, 9, and 10). Therefore, the probability of selecting a number greater than 7 after having selected the number 1 is:
- P(selecting a number greater than 7 after 1) = 3/9 = 1/3
Since these are independent events, we multiply the probabilities to find the overall probability:
- P(selecting a number less than 2 AND a number greater than 7) = (1/10) * (1/3) = 1/30
Converting this fraction to a percentage:
- 1/30 = 3.33% (approximately)
Looking at the given options, none of them match the correct probability. Therefore, there seems to be a discrepancy in the options provided and the actual probability calculation.