$100$ 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.

$100$ 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

Determine if the toppings are mutually exclusive.

$100$ 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

A student is chosen at random from the group who like soft cheese. Find the probability that they also like marmalade.

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 $P\left(A\cap B\right)$.

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

Determine whether or not events $A$ and $B$ are independent.

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

Determine whether or not events $A$ and $B$ are mutually exclusive.

Stefan rolls two $6$-sided dice at the same time. One die has three green sides and three black sides. The other die has sides numbered from $1$ to $6$.

Draw a tree diagram to represent this sequence of events.

Stefan rolls two $6$-sided dice at the same time. One die has three green sides and three black sides. The other die has sides numbered from $1$ to $6$.

Find the probability that Stefan rolls a $5$.

Stefan rolls two $6$-sided dice at the same time. One die has three green sides and three black sides. The other die has sides numbered from $1$ to $6$.

Find the probability that he rolls a number less than $3$.