From the Venn diagram below, find: 

$P\left(A\right|B)$

From the Venn diagram below, find: 

From the Venn diagram below, find: 

From the Venn diagram below, find: 

From the Venn diagram below, find: 

The probability that it will be sunny tomorrow is $\frac{4}{5}$. If it is sunny, the probability that the cafeteria will sell ice creams is $\frac{2}{3}$. If it is not sunny, the probability that the cafeteria will sell ice creams is $\frac{1}{3}$. Represent this information in a tree diagram of ice creams are independent events.

The probability that it will be sunny tomorrow is $\frac{4}{5}$. If it is sunny, the probability that the cafeteria will sell ice creams is $\frac{2}{3}$. If it is not sunny, the probability that the cafeteria will sell ice creams is $\frac{1}{3}$. Find the probability that it will be sunny and the cafeteria will sell ice creams.

The probability that it will be sunny tomorrow is $\frac{4}{5}$. If it is sunny, the probability that the cafeteria will sell ice creams is $\frac{2}{3}$. If it is not sunny, the probability that the cafeteria will sell ice creams is $\frac{1}{3}$. Determine if the sun shining and the selling of ice creams are independent events.

S is the event Tim is wearing shorts and R is the event it is raining. It is known that $\mathrm{P}\left(\mathrm{R}\right)=0.5, \mathrm{P}\left(\mathrm{S}\right|\mathrm{R})=0.2,$ and $\mathrm{P}\left(\mathrm{S}\right|\mathrm{R}\text{'})=0.8$. Represent this situation in a tree diagram.