A hockey match is played from 3 p.m. to 5 p.m. A man arrives late for the match. What is the probability that he misses the only goal of the match which is scored at the 20th minute of the match?
the game is 120 minutes long.
He misses the goal if he arrives during the last 100 minutes, so
p = 100/120
To find the probability that the man misses the only goal of the match, we need to consider the time period during which he arrives.
Given that the hockey match is played from 3 p.m. to 5 p.m., we have a total duration of 2 hours, or 120 minutes.
The only goal was scored at the 20th minute of the match.
If the man arrives after the 20th minute, then he would miss the goal. Therefore, we need to determine the probability that he arrives after the 20th minute.
The time interval from the start of the match to the 20th minute is 20 minutes. So, the probability that he arrives after the 20th minute is equal to the time remaining in the match divided by the total duration of the match.
The time remaining in the match after the 20th minute is 120 - 20 = 100 minutes.
Therefore, the probability that the man arrives after the 20th minute and misses the only goal is 100/120 = 5/6, which is approximately 0.8333, or 83.33%.
To find the probability that the man arrives late and misses the goal, we need to know the duration of the match and the arrival time of the man.
Duration of the match: The hockey match is played from 3 p.m. to 5 p.m., which means it lasts for 2 hours.
Arrival time of the man: We are not given the exact arrival time of the man, but we know that he arrives late.
To calculate the probability, we need to assume that the man's arrival time is randomly distributed within the duration of the match (3 p.m. to 5 p.m.).
To solve this problem, we need to compare the time the man arrives with the time the only goal of the match is scored. If the man arrives after the 20th minute (when the goal is already scored), then he will miss the only goal.
Let's assume that the man has an equal chance of arriving at any time between 3 p.m. and 5 p.m. (i.e., it is uniformly distributed within the duration of the match).
Now, let's calculate the probability. The probability of the man arriving after the 20th minute (missing the goal) can be calculated as:
(Total time after the 20th minute) / (Total duration of the match)
Total time after the 20th minute: The total time after the 20th minute can be calculated as 2 hours minus 20 minutes (since the match lasts for 2 hours). Converting the time to minutes, we have 120 minutes - 20 minutes = 100 minutes.
Total duration of the match: The duration of the match is 2 hours, which equals 2 hours * 60 minutes = 120 minutes.
Using these values, we can calculate the probability as:
Probability = (Total time after the 20th minute) / (Total duration of the match)
= 100 minutes / 120 minutes
= 5/6
= 0.8333
Therefore, the probability that the man arrives late and misses the only goal of the match is approximately 0.8333 or 83.33%.