Question

IV. La clase de Probabilidad y Estadística consta de 13 niños y 23 niñas. Para poder representar la escuela en las Olimpiadas se requiere sacar cuatro alumnos de manera aleatoria, hallar la probabilidad de: a) Seleccionar exactamente dos niñas y dos niños. b) Seleccionar cuatro niñas. c) Seleccionar por lo menos un niño. d) Seleccionar exactamente tres niñas y un niño​

Answer 1

a) Probability of 2 boys and 2 girls: (C(2,13) * C(2,23)) / C(4,36).

b) Probability of 4 girls: C(4,23) / C(4,36).

c) Probability of at least 1 boy: 1 - (C(4,23) / C(4,36)).

d) Probability of 3 girls and 1 boy: (C(3,23) * C(1,13)) / C(4,36).

To calculate the probabilities, we can use combinations and the total number of ways to choose 4 students from the class of 36 (13 boys + 23 girls).

a) The probability of selecting exactly two boys and two girls can be found by calculating the number of ways to choose 2 boys from 13 and 2 girls from 23, divided by the total ways to choose 4 students.

b) The probability of selecting four girls is the number of ways to choose 4 girls from the total number of girls (23), divided by the total ways to choose 4 students.

c) The probability of selecting at least one boy is the complement of selecting only girls. So, it's 1 minus the probability of selecting four girls.

d) The probability of selecting exactly three girls and one boy involves choosing 3 girls from 23 and 1 boy from 13, divided by the total ways to choose 4 students.

By calculating these probabilities, you can determine the likelihood of each scenario occurring in the random selection process.