Question

harper wanted to know if there was a connection between her coffee consumption and how well she slept that night. for weeks, harper recorded how many cups of coffee she drank in the morning and how many hours she slept that night.
the probability that a day is one when she drank 0 cups of coffee is 0.7, the probability that it is one when she slept at least 6 hours is 0.4, and the probability that it is one when she drank 0 cups of coffee and slept at least 6 hours is 0.1.
what is the probability that a randomly chosen day is one when she drank 0 cups of coffee or slept at least 6 hours?
write your answer as a whole number, decimal, or simplified fraction.
save answer

Explanation:

Step1: Recall the formula for \(P(A\cup B)\)

The formula for the probability of the union of two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event that she drank \(0\) cups of coffee and \(B\) be the event that she slept at least \(6\) hours.

Step2: Substitute the given values into the formula

We know that \(P(A) = 0.7\), \(P(B)=0.4\), and \(P(A\cap B)=0.1\).
Substitute these values into the formula: \(P(A\cup B)=0.7 + 0.4-0.1\).

Step3: Calculate the result

First, add \(0.7\) and \(0.4\): \(0.7+0.4 = 1.1\). Then subtract \(0.1\) from \(1.1\): \(1.1-0.1=1\).

Answer:

\(1\)