Answer :
Probability is defined as,
[tex]\text{Probability}=\frac{required\text{ outcome}}{possible\text{ outcome}}[/tex]Let the prob that a day is one he drank exactly 0 cups of coffee be P(A)
Let the probability that a day is when he slept 8 hours be P(B)
Let the probabilty that a day is one he drank exactly 0 cups of coffee or slept for 8 hours be P(C)
[tex]\begin{gathered} P(A)=0.2 \\ P(B)=0.3 \\ P(C)=0.4 \end{gathered}[/tex]Probability he drank 0 cups of coffee and slept for 8 hours is an independent event hence, can be represented below as,
[tex]P(A\text{ OR B) = P(A) }\times P(B)[/tex]Substituting the variables P(A) and P(B) into the given formula above,
[tex]P(A\text{ OR B) = 0.2 }\times\text{ 0.3 = 0.06}[/tex]Hence, the prob is 0.06.