Garrett wanted to know if there was a connection between his coffee consumption and how well he slept that night. For weeks, Garrett recorded how many cups of coffee he drank in the morning and how many hours he slept that night.6 hours 7 hours0 cups of coffee 7 101 cup of coffee 8 62 cups of coffee 5 13What is the probability that a randomly selected day is one when he drank exactly 1 cup of coffee or 0 cups of coffee?Simplify any fractions.
Question
Garrett wanted to know if there was a connection between his coffee consumption and how well he slept that night. For weeks, Garrett recorded how many cups of coffee he drank in the morning and how many hours he slept that night.6 hours 7 hours0 cups of coffee 7 101 cup of coffee 8 62 cups of coffee 5 13What is the probability that a randomly selected day is one when he drank exactly 1 cup of coffee or 0 cups of coffee?Simplify any fractions.
Solution
To solve this problem, we first need to determine the total number of days that Garrett recorded his coffee consumption and sleep hours.
From the data given:
- There were 7 days when he drank 0 cups of coffee and slept for 6 hours.
- There were 10 days when he drank 0 cups of coffee and slept for 7 hours.
- There were 8 days when he drank 1 cup of coffee and slept for 6 hours.
- There were 6 days when he drank 1 cup of coffee and slept for 7 hours.
- There were 5 days when he drank 2 cups of coffee and slept for 6 hours.
- There were 1 day when he drank 2 cups of coffee and slept for 7 hours.
Adding these up, we get a total of 37 days.
The question asks for the probability that a randomly selected day is one when he drank exactly 1 cup of coffee or 0 cups of coffee.
- The number of days when he drank 0 cups of coffee is 7 + 10 = 17 days.
- The number of days when he drank 1 cup of coffee is 8 + 6 = 14 days.
So, the total number of days when he drank either 0 or 1 cup of coffee is 17 + 14 = 31 days.
The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes.
So, the probability that a randomly selected day is one when he drank exactly 1 cup of coffee or 0 cups of coffee is 31/37. This fraction cannot be simplified further.
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