A digital clock displays military time in hh:mm format. Find the probability that the number made up of the first two digits on the clock is less than 25.
Answer (2)
The probability that the hour displayed on a military time clock is less than 25 is always 1, as all possible hours are from 00 to 23. Therefore, all outcomes are favorable. This means that you can be certain that the first two digits (the hour) will always be less than 25.
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The hour in military time ranges from 00 to 23.
There are 24 possible outcomes for the hour.
All possible hours (00-23) are less than 25.
The probability that the hour is less than 25 is 1 .
Explanation
Understand the problem and provided data The problem asks for the probability that the hour displayed on a digital clock in military time (hh:mm) is less than 25. Since military time ranges from 00:00 to 23:59, the possible values for the hour (hh) are 00, 01, 02, ..., 23.
Determine the total number of possible outcomes The total number of possible outcomes for the hour (hh) is the number of values from 00 to 23, inclusive. This is a total of 24 possible outcomes.
Determine the number of favorable outcomes We want to find the number of favorable outcomes, where the hour (hh) is less than 25. Since the maximum possible hour in military time is 23, all possible hours are less than 25. Therefore, all 24 possible outcomes are favorable.
Calculate the probability The probability that the hour (hh) is less than 25 is the number of favorable outcomes divided by the total number of possible outcomes: P ( hh < 25 ) = Total number of outcomes Number of favorable outcomes = 24 24 = 1
State the final answer Therefore, the probability that the number made up of the first two digits on the clock is less than 25 is 1.
Examples
This type of probability problem can be used to understand the likelihood of events occurring within a specific time frame. For example, if you are analyzing data that is recorded using military time, you might want to know the probability that an event occurred before a certain hour. Understanding this probability can help you make informed decisions based on the time of day.
