Rose Harrison and Clara Huizink Solutions for Exercise 20: Mixed practice

A bag contains four calculators $\left(C\right)$ and six protractors $\left(P\right)$. One item is taken from the bag at random and not replaced. A second item is then taken at random.

Complete the tree diagram by writing probabilities in the spaces provided.

A typical teenager should consume approximately $2000$ calories per day. A survey of $120$ students, three-fifths of which were male, revealed the following:

$80$ students ate more than the recommended
amount.
Half of the girls ate less than the recommended amount.
Five-sixths of the boys ate more than the recommended amount.

The same number of boys as girls ate the recommended amount of calories.

Calculate the probability that a student selected at random ate the recommended amount of calories.

A typical teenager should consume approximately $2000$ calories per day. A survey of $120$ students, three-fifths of which were male, revealed the following:

$80$ students ate more than the recommended amount.
Half of the girls ate less than the recommended amount.
Five-sixths of the boys ate more than the recommended amount.

The same number of boys as girls ate the recommended amount of calories.

Calculate the probability that a student selected at random is male and ate less than the recommended amount.

A typical teenager should consume approximately 2000 calories per day. A survey of 120 students, three-fifths of which were male, revealed the following:

80 students ate more than the recommended
amount.
Half of the girls ate less than the recommended amount.
Five-sixths of the boys ate more than the recommended amount.

The same number of boys as girls ate the recommended amount of calories.

Calculate the probability that a student selected at random ate more than the recommended amount given that they are female.

In a group of $50$ people, $10$ are healthy and the rest have either high blood pressure, high cholesterol or both; $23$ people have high blood pressure and $28$ have high cholesterol. Find the probability that a person selected at random has high blood pressure.

In a group of $50$ people, $10$ are healthy and the rest have either high blood pressure, high cholesterol or both; $23$ people have high blood pressure and $28$ have high cholesterol. Find the probability that a person selected at random has high blood pressure and high cholesterol 

In a group of $50$ people, $10$ are healthy and the rest have either high blood pressure, high cholesterol or both; $23$ people have high blood pressure and $28$ have high cholesterol. Find the probability that a person selected at random has high blood pressure or high cholesterol.

In a group of $50$ people, $10$ are healthy and the rest have either high blood pressure, high cholesterol or both; $23$ people have high blood pressure and $28$ have high cholesterol. Find the probability that a person selected at random has high cholesterol only.