a football match was played for two hours. a man arrives late for the match. what is the probability that he misses the only goal of the match which is scored at 30th minute of the match?
Since the 30th minute is at the end of the 1st quarter, there is a 3/4 probability that he missed the goal.
To calculate the probability that the man misses the only goal of the match, we need to determine the time interval during which he arrives.
If the man arrives anytime before the 30th minute, he will not miss the goal. However, if he arrives anytime after the 30th minute, he will miss the goal. Thus, we need to find the probability that he arrives after the 30th minute.
Since the football match is played for two hours, which is equivalent to 120 minutes, we can represent the arrival time as a number between 31 and 120 (inclusive). The total number of possible arrival times is therefore 120 - 30 = 90.
The total number of outcomes, which represents all possible arrival times, is 120 because the man could arrive at any minute between 1 and 120.
Therefore, the probability that the man arrives after the 30th minute and misses the only goal of the match is 90/120.
Simplifying this fraction, we get 3/4, which means there is a 75% chance that the man misses the only goal of the match.