A mother has two children. What is the probability that both are girls?

Solution 1 Sample Space ={BB, BG, GG } So, 1/3

Solution 2 Sample Space ={BB, BG, GB, GG } So, 1/4

Which is correct? Suppose the problem is changed to

"A mother is pregnant and is going to have two children. What is the probability that both are girls?"

Which should be the correct solution from above?

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
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Comments

Let's use an analogy here:

If you toss a fair coin twice. The probability of getting both heads or both tails is (obviously) the same. But is it also equal to the probability of getting a head and a tail (not necessarily in that order) too?

Or you could ask: Why was GB omitted from the sample space in Solution 1?

Pi Han Goh - 3 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$