Final answer:
The probability of the burglar hitting the correct sequence to open the door on a keypad with digits 0-9 is 1/100,000, as each of the five presses has a 1/10 chance of being correct, resulting in a combined probability of (1/10)^5.
Step-by-step explanation:
The subject of this question is probability, which falls under the category of Mathematics. The student's question can be addressed by calculating the chance of selecting a correct sequence of five digits on a keypad where each digit can be a number from 0-9.
To calculate the probability of the burglar hitting the sequence to open the door correctly, we have to consider that each button press is an independent event and that for each press, there are 10 possibilities (the digits 0 through 9). Therefore, the probability for each individual button press is 1 in 10 (or 1/10).
Since there are five button presses, all of which must be correct and in the correct order, the probability of achieving the correct sequence is (1/10) × (1/10) × (1/10) × (1/10) × (1/10), which equals 1/100,000. This is one possibility out of the total number of possible combinations, which is 10 to the power of 5 (10⁵) or 100,000.