In China, where many couples were allowed to have only one child, the probability of a baby being a boy was 0.545. Among six randomly selected births in China, what is the probability that at least one of them is a girl? Could this system continue to work indefinitely? (Phasing out of this policy was begun in 2015.)

Question

Octavio Vargas

Mathematics

13 September, 23:12

In China, where many couples were allowed to have only one child, the probability of a baby being a boy was 0.545. Among six randomly selected births in China, what is the probability that at least one of them is a girl? Could this system continue to work indefinitely? (Phasing out of this policy was begun in 2015.)

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Greyson · Answer 1

Answer: 0.9738

Step-by-step explanation:

This is solved by the probability distribution formula for random variables where probability of determining random variable X is given by

P (X=r) = nCr * p^r * q^n-r

Where n = number of sample = 6

p = probability of success = 0.545

q = 1-p = 0.455

r = possible outcome from number of sample.

If 6 random births are chosen, Probability that at least 1 of them is a girl = 1 - [probability that none of them is a girl] = 1 - [probability that all 6 kids are boys]

Probability that all 6 kids are boys = 6C6 * 0.545^6 * 0.455^0 = 0.0262

Probability that at least one is a girl = 1 - 0.0262 = 0.9738.