Draw one number from the set of two‑digit numbers made of digits {3, 5, 7}. Write elements of the sample space of elementary events Ω, knowing that digits can be repeated. Calculate the probabilityprobabilityprobability of drawing a number greater than 55.

Open the interactive illustration that describes the tree diagram methodtree diagram methodtree diagram method and watch it carefully.

There are three blue cardboard pieces and two yellow cardboard pieces on the table. Next to them, there are two boxes. In box A, there is one blue piece and in box B, there is one yellow and four blue pieces. If we take a blue piece from the table, we draw from box A, if yellow – from box B. What is the probability of an event A – that we get two pieces in the same colour?

$P\left(A\right)=\frac{3}{5}·\frac{1}{2}+\frac{2}{5}·\frac{1}{5}=\frac{3}{10}+\frac{2}{25}=\frac{30}{100}+\frac{8}{100}=\frac{38}{100}=0,38$

Probability of the event A is 0,38.

Do the exercise using the classical definition of probabilityprobabilityprobability.

We roll a symmetric, six‑sided dice two times. Calculate the probability of getting a number not smaller than 4 both times.

Do the exercise using the tree diagram method.

We roll a symmetric, six‑sided dice two times. Calculate the probability of getting a number not smaller than 4 both times.

Do the exercise using the tree diagram methodtree diagram methodtree diagram method.

There are five blue beads and two golden beads in a sack. We take out two beads and do not put them back. Calculate the probabilityprobabilityprobability of taking out two beads of the same colour.

Do the exercise using the tree diagram method.

While flipping a non‑symmetric coin, the probability of getting heads is equal to $\frac{{\displaystyle 2}}{3}$, and tails $\frac{{\displaystyle 1}}{3}$. Calculate the probability of getting at least one heads in two trials.

An extra task:

There were three times less winning tickets than empty tickets in the box, during the lottery. The probability of getting one winning ticket and one empty ticket is $\frac{{\displaystyle 45}}{119}$.

Kasia takes part in a language contest where the questions can be in English or in French. The choice of language is done by drawing lots. If the chosen language is French, then the probability of Kasia winning the price is equal to 0,5 and if it is English, then the probability is equal to 0,9. What is the probability of Kasia winning the price?

From the senior year of high school, 85% of all girl and 95% or all boys declared that they will continue education at universities after their final exams. The number of boys is 60% of all senior students. Draw a tree illustrating this experiment and describe it in English. Calculate the probability of an event where a randomly chosen person from this group decides to continue education at university. Write the answer in English.