We are told that having a male child and female child are independent events both with a probability of $0.5 .$ A couple has $4$ male children, and we are asked to verify if there is a greater probability that the next child will be a female child.

We can break up this situation into two cases.

The next child will be female.
The next child will be male.

Because we know that the events are independent, we can multiply the probabilities to find the chances of having

4

male children and a female child. Let's do it!

P (M) \cdot P (M) \cdot P (M) \cdot P (M) \cdot P (F)

SubstituteII

$P (M) = 0.5$ , $P (F) = 0.5$

0.5 \cdot 0.5 \cdot 0.5 \cdot 0.5 \cdot 0.5

MultPow

$a^{m} \cdot a^{n} = a^{m + n}$

0 . 5^{5}

CalcPow

Calculate power

0.03125

We can use the same procedure to find the probability of having

5

male children.

P (M) \cdot P (M) \cdot P (M) \cdot P (M) \cdot P (M)

Substitute

$P (M) = 0.5$

0.5 \cdot 0.5 \cdot 0.5 \cdot 0.5 \cdot 0.5

MultPow

$a^{m} \cdot a^{n} = a^{m + n}$

0 . 5^{5}

CalcPow

Calculate power

0.03125

We can see that the probability for both cases is the same. Therefore, the probability that the next child will be a female child is no greater than the probability that the next child will be a male child.

Exercise 3 Page 713

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