Let the random variable X denote the number of girls

dohtarjev510

dohtarjev510

Answered question

2022-02-14

Let the random variable X denote the number of girls in a five-child family. If the probability of a female birth is 0.5, what are the probabilities of having 0, 1, 2, 3, 4, and 5 girls?

Answer & Explanation

Bordadwayjpf

Bordadwayjpf

Beginner2022-02-15Added 17 answers

Step 1
The probability of having a girl is given as 0.5. This means that the probability of not having a girl is also 0.5.
The last thing to look at is the number of ways we can achieve any given result. For instance, there is only 1 way to have 0 girls (and the same goes for 5 girls), but there are 5 different ways we can have 1 girl (and the same goes for 4 girls). This is a combinations question, with:
Cn, k=(nk)=n!(k!)(nk)! with n=population, k=picks
Boiling it all down, we end up with:
0 girls =(50)(12)0(12)5=1×1×132=132
1 girls =(51)(12)1(12)4=5×12×116=532
2 girls =(52)(12)2(12)3=10×14×18=1032=516
3 girls =(53)(12)3(12)2=10×18×14=1032=516
4 girls =(54)(12)4(12)1=5×116×12=532
5 girls =(55)(12)5(12)0=1×132×1=132
Notice that if we add all of these up, we get 1 (or the sum total of all probabilities):
132+532+1032+1032+532+132=3232=1

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