Rishi S. answered • 06/26/23
Stanford Undergrad Specializing In Math and Test Prep
The time it takes to wash the dishes is said to be uniformly distributed between 8 minutes and 18 minutes. In a uniform distribution, the probability of any particular event occurring is the same throughout the range. In other words, any minute spent washing dishes is just as likely as any other.
First, let's understand the total range of time it can take to wash the dishes. This is given by the difference between the maximum time (18 minutes) and the minimum time (8 minutes), which is 18 - 8 = 10 minutes.
1. **What is the probability that washing dishes tonight will take me between 11 and 15 minutes?**
To find this, we first calculate the range of time between 11 minutes and 15 minutes, which is 15 - 11 = 4 minutes.
In a uniform distribution, the probability is given by the ratio of the desired outcome range (4 minutes in this case) to the total range (10 minutes in this case).
So, the probability is 4 minutes / 10 minutes = 0.4.
As a fraction, this is 4/10, which simplifies to 2/5.
To three decimal places, this is 0.400.
2. **What is the probability that washing dishes tonight will take exactly 11 minutes?**
In continuous distributions (like this uniform distribution), the probability of an event taking exactly a specific amount of time (like exactly 11 minutes) is always zero. This is because there are infinite possibilities within any range of time, making the probability of hitting exactly one specific time point zero. So, no matter how long it takes you to wash the dishes, the probability it will take exactly 11 minutes is 0.
