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pantera1 [17]
3 years ago
15

Suppose you know that Mr. and Mrs. Vincent have at most eight children. One day you happen to meet two girls who were the Vincen

t children. When you told the Vincents about this they told you that the chance of this happening is exactly 1/2, i.e., the probability that two of the Vincent children, randomly chosen, are both girls is exactly 1/2. How many children do the Vincent’s have, exactly? Of them what is the exact number of girls?
Mathematics
1 answer:
lianna [129]3 years ago
3 0

Answer:

The number of children are 4 out of which 3 are girls

Step-by-step explanation:

Data provided in the question:

P(Two randomly selected children are girls) = \frac{1}{2}

now,

let the number of children be 'n'

the number of girls be 'x'

thus,

P(Two randomly selected children are girls) = \frac{^xC_2}{^nC_2} = \frac{1}{2}

also,

^nC_r = \frac{n!r!}{(n-r)!}

thus,

\frac{\frac{x!2!}{(x-2)!}}{\frac{n!2!}{(n-2)!}} = \frac{1}{2}

or

\frac{x(x-1)}{n(n-1)}=\frac{1}{2}

or

2x(x-1) = n(n-1)

now

for x = 3 and n = 4

i.e

2(3)(3-1) = 4(4-1)

12 = 12

hence, the relation is justified

therefore,

The number of children are 4 out of which 3 are girls

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