__Today there is a 60% chance of rain, a 30% chance of lightning, and a 15% chance of lightning and rain together.__

__1) Determine if rain today and lightning today are independent events?__

*A)The two events are independent because P(lightning) ⋅ P(rain) = 0.15 does not equal P(lightning and rain) = 0.18.*

*B)The two events are not independent because P(lightning) ⋅ P(rain) = 0.15 does not equal P(lightning and rain) = 0.18.*

*C)The two events are independent because P(lightning) ⋅ P(rain) = 0.18 does not equal P(lightning and rain) = 0.15*

*D)The two events are not independent because P(lightning) ⋅ P(rain) = 0.18 does not equal P(lightning and rain) = 0.15*

**2) Now suppose that today there is a 60% chance of rain, a 30% chance of lightning, and a 10% chance of lightning if it’s raining. What is the chance of both rain and lightning today?**

*A)3%*

*B)6%*

*C)12%*

*D)18%*

kalabmath Mar 29, 2019

#1**+1 **

\(\text{If rain and lightning are independent then }\\ P[\text{rain AND lightning}]=P[\text{rain}]P[\text{lightning}]\\ 0.15 \neq 0.6 \cdot 0.3 = 0.18\\ \text{that's choice C}\)

\(P[\text{rain AND lightning}] = \\ P[\text{lightning |raining}]P[\text{raining}] = \\ (0.1)(0.6) = 0.06 = 6\%\\ \text{Choice B}\)

.Rom Mar 29, 2019