Question

Anthony, an aspiring meteorologist, spent the past few weekends studying the clouds. He took detailed notes on the types of clouds observed and the time of day they were observed. Stratocumulus Stratus Morning 4 1 Afternoon 3 7. 8 4 Evening What is the probability that a randomly selected cloud was observed in the afternoon or morning? Simplify any fractions.

Answer 1

The searched probability is

`P(\text{AFTERNOON }\cup\text{ MORNING)}`

is given by

`P(\text{AFTERNOON }\cup\text{ MORNING)}=\text{ }P(\text{AFTERNOON )}+P(\text{ MORNING)-}P(\text{AFTERNOON }\cap\text{ MORNING)}`

which gives

`P(\text{AFTERNOON }\cup\text{ MORNING)}=P(\text{AFTERNOON )}+P(\text{ MORNING)}`

because the events "afternoon" and "morning" are mutually exclusive. Then, we get

`\begin{gathered} P(\text{AFTERNOON }\cup\text{ MORNING)}=(5)/(27)+(10)/(27) \\ P(\text{AFTERNOON }\cup\text{ MORNING)}=(15)/(27) \end{gathered}`

then, the answer is 15/27