# Probability: math exercises in 2nd grade corrected in PDF.

Second grade math exercises on probability.

Exercise #1:

1.
a. Perform 50 throws of two coins.
For each throw, note the event that is performed:
A: “Get two tails”;
B:Get two sides;
C: Get one head and one tail”.

b. Calculate the frequency of each of the events A, B and C.

2. Perform a new series of 50 throws and also calculate the frequencies of A, B and C.
Exercise #2:

Propose a way to simulate the drawing of 20 students among 832 students in a high school.
Exercise #3:

In some countries, it is recommended that couples wishing to start a family have children until both sexes are represented.

1. Give a way to simulate the composition of a family obeying this policy.

2.
a. Carry out 100 simulations and note, each time, the number of children in the family.
b. Calculate, for the sample obtained, the average number of children per family.
Exercise #4:

We throw a balanced die and we are interested in the number of throws necessary to obtain the six digits .
For example, the realization: 2 3 5 3 4 2 6 3 5 6 2 4 4 1 required 14 throws to get all six digits.

a. Perform simulations of this experiment to obtain the six numbers.

b. Estimate the average number of throws required to obtain the six digits.

Exercise #5:

Here are the first 100 digits of the decimal form of Pi:

3,1415 92653 58979 32384 62643

38327 95028 84197 16939 93751

05820 97494 45923 07816 40628

62089 98628 03482 53421 17067

1- We take at random one of the first 30 numbers.

Determine the probability that it is :

a-0 b-1 c-2 d-3

Exercise #6:

2- Repeat question 1 with :

a- the first 50 digits

b- the first 100 digits.

In a lottery, a wheel is divided into identical sectors:
Nine of these areas earn \$5, six earn \$10, three earn \$50, two earn \$100 and four earn nothing.

2) What is the probability of winning at least 50€? Justify your answer.

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