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.

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 $\mathrm{P}\left(\mathrm{S}\right|\mathrm{R}\text{'})=0.8$. Use both Theorem 2 to verify that events $S$ and $R$ are not independent.

Sahar is trying to determine if being tall (here defined as being $180$ cm or more) is somehow related to liking basketball. She surveyed $70$ students, $30$ of which were over $180 \mathrm{cm}$. $48$ students surveyed like basketball, $29$ of which were under $180 \mathrm{cm}$. Draw a two-way table to represent this.

Sahar is trying to determine if being tall (here defined as being $180$ cm or more) is somehow related to liking basketball. She surveyed $70$ students, $30$ of which were over $180 \mathrm{cm}$. $48$ students surveyed like basketball, $29$ of which were under $180 \mathrm{cm}$. Find P(tall).

Sahar is trying to determine if being tall (here defined as being $180$ cm or more) is somehow related to liking basketball. She surveyed $70$ students, $30$ of which were over $180 \mathrm{cm}$. $48$ students surveyed like basketball, $29$ of which were under $180 \mathrm{cm}$. Find P(not tall likes basketball).

Sahar is trying to determine if being tall (here defined as being $180$ cm or more) is somehow related to liking basketball. She surveyed $70$ students, $30$ of which were over $180 \mathrm{cm}$. $48$ students surveyed like basketball, $29$ of which were under $180 \mathrm{cm}$. Are the events being tall' and 'liking basketball' independent? Justify your answer.

In a netball match there are $14$ players on the court: $8$ have brown hair and $6$ have blue eyes. There are $4$ students who have neither brown hair nor blue eyes. Let $\mathrm{H}$ be the event has brown hair and $\mathrm{B}$ be the event 'has blue eyes. Draw a Venn diagram to represent this.