A couple plans to have four children. Using a tree diagram , obtain the sample space. Then, find the probability that the family has three boys first and then one girl.
And I have four answers to choose from ...
3/16
1/6
1/8
1/16
2007-05-09 15:21:21 · 7 answers · asked by baby_girl_clover 1 in Science & Mathematics ➔ Mathematics
1/16.
Your tree diagram will have two nodes at the top: boy first, girl first.
Under each "boy first" and "girl first" you'll have "boy second" and "girl second", for four nodes in the second level.
Under each of those four nodes, you'll have "boy third" and "girl third", for eight nodes on the third level.
Under each of those eight nodes, you'll have "boy fourth" and "girl fourth", for sixteen nodes on the fourth level.
You'll have sixteen paths in your tree diagram, and only one of the sixteen goes boy - boy - boy - girl. This demonstrates that the probability is 1/16.
Note: If the question were "three boys and one girl IN ANY ORDER" the answer would be 1/4 instead. (Because three additional paths -- girl - boy - boy - boy; boy - girl - boy - boy; boy - boy - girl - boy -- involve three boys and one girl. But since the order is specified, there is only one matching path out of sixteen.)
2007-05-09 15:27:23 · answer #1 · answered by McFate 7 · 0⤊ 0⤋
1/16
2007-05-09 15:31:41 · answer #2 · answered by rwbblb46 4 · 0⤊ 0⤋
3/16
2007-05-09 15:27:52 · answer #3 · answered by Subodh 2 · 0⤊ 0⤋
I think it's 1/16 because there is a 1/2 chance that they will get their perferred gender each time they have a baby. You multiply 1/2 chance by four kids and you get 1/16
2007-05-09 15:28:39 · answer #4 · answered by bibliohile 1 · 0⤊ 0⤋
-------------------B - BBBB (1)
------------B < G - BBBG (2)
-----B < ------ B - BBGB (3)
---/ ------ G < G - BBGG (4)
B --------------- B - BGBB (5)
---\ ------- B < G - BGBG (6)
-----G < -------- B - BGGB (7)
------------ G < G - BGGG (8)
------------------ B - GBBB (9)
------------B < G - GBBG (10)
-----B < ----- B - GBGB (11)
---/ ----- G < G - GBGG (12)
G ------------- B - GGBB (13)
---\ ------ B < G - GGBG (14)
-----G < ------- B - GGBB (15)
------------ G < G - GGGG (16)
the sample space, therefore is 16 .
there' s only ONE occurrence of three boys first then 1 girl which is sample (2) - BBBG, out of 16 possible outcome.
thus the probability is 1/16.
2007-05-09 15:45:56 · answer #5 · answered by michael_scoffield 3 · 0⤊ 0⤋
i am really good at math and i think it is 1/16
2007-05-09 15:44:20 · answer #6 · answered by Anonymous · 0⤊ 0⤋
this question is seemingly retarded but i'll go and say 3/16
2007-05-09 15:27:59 · answer #7 · answered by blu_aut_fox 1 · 0⤊ 0⤋