The Patterson family has 3 kids, 1 boy and 2 girls. Suppose that for each birth, the probability of a boy birth is 1/2, and the probability of a girl birth is also 1/2. What is the fractional probability of having 1 boy and 2 girls, in any order, in a family's first 3 births?

Question

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Respuesta :

MrRoyal MrRoyal · Answer 1 · 2020-08-24T18:58:16+02:00

Answer:

[tex]Probability = \frac{1}{8}[/tex]

Step-by-step explanation:

Given

Represent Boys with B and Girls with G

[tex]P(B) = \frac{1}{2}[/tex]

[tex]P(G) = \frac{1}{2}[/tex]

Required

Find the probability or having 1 boy 2 girls

Since the order is not important, the probability is calculated as follows;

[tex]Probability = P(B) * P(G) * P(G)[/tex]

Substitute [tex]\frac{1}{2}[/tex] for P(B) and P(G)

[tex]Probability = \frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex]

[tex]Probability = \frac{1 * 1 * 1}{2 * 2 *2}[/tex]

[tex]Probability = \frac{1}{8}[/tex]

Hence, the fractional probability is [tex]\frac{1}{8}[/tex]