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Assuming that the chance of a baby being a boy or a girl is the same, calculate the following probabilities for a family with 3 children:a. Calculate the probability that a family with three children has: Question 1i. Pr(all males) =

Question

Assuming that the chance of a baby being a boy or a girl is the same, calculate the following probabilities for a family with 3 children:a. Calculate the probability that a family with three children has: Question 1i. Pr(all males) =

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Solution

Claro, vamos a resolver el problema paso a paso.

Primero, definamos el problema:

  • La probabilidad de que un bebé sea niño (m) es 0.5.
  • La probabilidad de que un bebé sea niña (f) es 0.5.
  • Queremos calcular la probabilidad de que una familia con tres hijos tenga todos los hijos varones.

Para resolver esto, necesitamos calcular la probabilidad de que los tres hijos sean varones.

  1. La probabilidad de que el primer hijo sea varón es 0.5.
  2. La probabilidad de que el segundo hijo sea varón es 0.5.
  3. La probabilidad de que el tercer hijo sea varón es 0.5.

Como los eventos son independientes, multiplicamos las probabilidades individuales:

Pr(all males)=0.5×0.5×0.5 \text{Pr(all males)} = 0.5 \times 0.5 \times 0.5

Pr(all males)=0.53 \text{Pr(all males)} = 0.5^3

Pr(all males)=0.125 \text{Pr(all males)} = 0.125

Por lo tanto, la probabilidad de que una familia con tres hijos tenga todos los hijos varones es 0.125 o 12.5%.

This problem has been solved

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