SOLUTION: n a family with 5 children what is the probability of having 3 boys and then 2 girls, in that order?

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Question 1191940: n a family with 5 children what is the probability of having 3 boys and then 2 girls, in that order?
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
You're asking for the probability of the fourth birth order
in the list below of all 32 possible birth orders.

There is only 1 successful birth orders out of those 32 possible
birth orders listed below. 

The number of possible birth orders is 32 because:

There are 2 ways that the 1st birth could turn out.
There are 2 ways that the 2nd birth could turn out.
There are 2 ways that the 3rd birth could turn out.
There are 2 ways that the 4th birth could turn out.
There are 2 ways that the 5th birth could turn out.

2x2x2x2x2 = 25 = 32

1. BBBBB
2. BBBBG
3. BBBGB
4. BBBGG   <--The only successful birth order.
5. BBGBB
6. BBGBG
7. BBGGB
8. BBGGG
9. BGBBB
10. BGBBG
11. BGBGB
12. BGBGG
13. BGGBB
14. BGGBG
15. BGGGB
16. BGGGG
17. GBBBB
18. GBBBG
19. GBBGB
20. GBBGG
21. GBGBB
22. GBGBG
23. GBGGB
24. GBGGG
25. GGBBB
26. GGBBG
27. GGBGB
28. GGBGG
29. GGGBB
30. GGGBG
31. GGGGB
32. GGGGG

So what fraction represents 1 SUCCESSFUL way 
out of 32 POSSIBLE ways?

Edwin

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


For each birth, the probability is 1/2 that it is a boy and 1/2 that it is a girl.

The probability of ANY specified sequence of five births is (1/2)^5 = 1/32.

ANSWER: 1/32