Question 2

The probability that there are no repeated digits in a three-digit PIN is 0.72.

To calculate the probability that a randomly selected three-digit PIN using the digits 0–9 has no repeated digits, we find the total number of possible combinations and the favorable outcomes. The total combinations for a three-digit PIN where digits can be repeated is 10^3 (1000). For no repetition, the first digit has 10 options, the second has 9, and the third has 8, giving us 10 * 9 * 8 = 720 favorable outcomes. Therefore, the probability is 720/1000, which simplifies to 0.72.

A) 0.72

This option is correct as it accurately reflects the probability of selecting a three-digit PIN with no repeated digits. The calculation shows that there are 720 valid combinations out of 1000 total combinations, leading to a probability of 0.72.

B) 0.7

Option B is incorrect because it underestimates the probability of selecting a three-digit PIN without repeated digits. The accurate calculation yields 0.72, not 0.7, making this option an inaccurate representation of the probability.

C) 0.3

This option is incorrect as it significantly misrepresents the probability of selecting a three-digit PIN with no repeated digits. The calculation indicates a much higher probability of 0.72, thus making this option not viable.

D) 1

Option D is incorrect because a probability of 1 would suggest that every randomly selected PIN must have no repeated digits, which is not the case. Given the total combinations, the probability is actually 0.72, indicating that while it is likely, it is not guaranteed.

Conclusion

The correct answer of 0.72 accurately represents the probability of selecting a three-digit PIN with no repeated digits, derived from the proper calculation of favorable outcomes over total outcomes. All other options fail to reflect the mathematical reality of the situation, either underestimating or overestimating the likelihood of no repeated digits in the PIN.