Rose Harrison and Clara Huizink Solutions for Exercise 17: Mixed practice

A group of $30$ students were asked about their favourite way of eating eggs.

• $18$ liked boiled eggs$\left(B\right)$
• $10$ liked fried eggs$\left(F\right)$
• $6$ liked neither

Find $P\left(F\right)$.

A group of $30$ students were asked about their favourite way of eating eggs.

• $18$ liked boiled eggs$\left(B\right)$
• $10$ liked fried eggs$\left(F\right)$
• $6$ liked neither

Find $P\left(B\text{'}\cup F\text{'}\right)$ in simplest form of fraction.

A group of $30$ students were asked about their favourite way of eating eggs.

• $18$ liked boiled eggs$\left(B\right)$
• $10$ liked fried eggs$\left(F\right)$
• $6$ liked neither

Find $P\left(B\cap F\right)$ in simplest fraction.

A group of $30$ students were asked about their favourite way of eating eggs.

• $18$ liked boiled eggs$\left(B\right)$
• $10$ liked fried eggs$\left(F\right)$
• $6$ liked neither

A student chosen at random likes boiled eggs. Find the probability that the student also likes fried eggs.

A survey was carried out an international airport. Travellers were asked their fight destination and results are shown in the table.

One traveller is chosen at random. Find the probability in simplest form of fraction that this traveller is going to Vienna.

$P\left(A\right)=0.5, P\left(B\right)=0.6$ and $P\left(A\cup B\right)=0.8$. Find $P\left(A\cap B\right)$.

$100$ students were asked if they liked various toast toppings.

• $56$ like avocado
• $38$ like marmalade
• $22$ like soft cheese
• $16$ like avocado and marmalade, but not soft cheese
• $8$  like soft cheese and marmalade, but not avocado
• $3$  like avocado and soft cheese, but not marmalade
• $4$ like all three toppings

Find the number of students who didn't like any topping.

Events $A$ and $B$ have probabilities $P\left(A\right)=0.4, P\left(B\right)=0.65$ and $P\left(A\cup B\right)=0.85$. Calculate $P\left(A\cap B\right)$.