## hwyl one year ago challenge! ready?

1. hwyl

2. hwyl

solve without using complement, that is $$\sf P(x) = 1 - P(x')$$

3. anonymous

1/5?

4. hwyl

@UsukiDoll

5. anonymous

Probability of at least 1 girl $P(X \ge 1)=P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)$

6. UsukiDoll

I don't do stats problems.

7. anonymous

probability of 1 girl + probability of 2 girls + probability of 3 girls + probability of 4 girls + probability of 5 girls

8. hwyl

continue

9. anonymous

can i do it as well

10. hwyl

are you using $$\large \cup_{x=1} ^{n} X_i = P(x_1 \cup x_2 \cup x_3\cup x_4 \cup x_5)$$

11. anonymous

$P(X \ge 1)=\frac{1}{32}+\frac{1}{16}+\frac{1}{8}+\frac{1}{4}+\frac{1}{2}=\frac{1+2+4+8+16}{32}=\frac{31}{32}$ another method $P(X=0)=\frac{1}{32}$$P(X \ge 1)=1-P(X=0)=1-\frac{1}{32}=\frac{32-1}{32}=\frac{31}{32}$

12. hwyl

haha wow

13. hwyl

i said without using complement

14. anonymous

I've done both with and without compliment, the compliment method is much faster anyway

15. Michele_Laino

another equivalent reasoning, can be this: the even space contains 32 possible events, nevertheless only one event, of them, is like this: BBBBB, where B stands for boy, so the total number of favorable events is 31

16. anonymous

I think you can also do this using binomial distribution where n=5 p=q=0.5

17. anonymous

why do u people make ur life so hard

18. Michele_Laino

oops..event space

19. hwyl

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20. hwyl

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