probability distribution for children

S

Sonja

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If someone could maybe help me strat this i have no idea where to begin or end at that??

Q. Suppose that a newly married couple is planning to have two children, and is interested in knowing the probabilities of having no girls, one girl, or two girls. Assume that the probability of having a girl is .50 in any one birth.

Construct a probability distribution of the random variably x, where x is the number of girls born to this couple.

Please help I have no clue where to start...anything will help
 
Probability of a girl in single birth, P = .5
then probability of a boy or non girl Q is .5

probability of two girls in two births=PP
Probability of only one girl in two births is first birth a boy and second birth a girl, OR first birth a girl and second birth a girl
QP OR PQ
[when you say OR you add, when you say AND you multiply]
probability only one girl in two births = 2PQ

Probability of no girls=QQ

....x.......Probability
....0...........Q^2
.....1.........2PQ
......2..........P^2

Arthur
 
Sorry Arthur can you maybe elaborate on that a bit more. Im really new at this math stuff and haven't been in school for awhile this is an intro course im taking so im not quite familiar with the math slang
i don't know what ^ this thing is lol
im a newbie i know.lol
please get back to me
Sonya
 
Sonia-
I posted a answer explaining what we use the symbol ^ for, "to the power of"
I also noted that you have someone helping you with a great deal of detail.
I do not want to add to your confusion, because he is so detailed in his aid.
I will point out three things:
1) the coefficient N!/[{K!}{N-K}!] are the same as PASCALS triangle, if you are familiar with this. If not forget about this hint.

2) 2 or more , means probability of 2 OR probability of 3 OR etc
when you say OR you add when you say AND you multiply
Then 2 or more is the sum as you stated from x=2 to x=7

3) "2 or more" is the same as "not 0 or 1"
1 - [Q^7+7P^1Q^6]
1- {7!/0!7!} P^0Q^7 - [7!/1!6!]P^1Q^6

If this is confusing , forget about it and just deal with the other person answering you

Pascals triangle
................................................ 1
................................................1..1
...............................................1..2..1
..............................................1..3..3...1
.............................................1..4..6...4..1
...........................................1...5..10.10.5...1
.........................................1...6...15.20..15..6..1
.......................................1....7..21..35..35..21.7..1
the last row are the coefficients of [p+Q]^7

Arthur
 
Sonia I got you confused with another student
^ means to the power of
a^2 means a squared
a^3 means a cubed
a^4 means a raised to the fourth power
a^2 is a times a
a^3 is a times a times a

with two births the chance that both births are girls is P times P or P^2,P squared
the chance of both boys is Q^2 or not a girl[Q] times not a girl [Q]
the probability of a boy and a girl birth can happen two ways. the first birth a boy and the second a girl [Q times P] or the first birth a girl and the second a boy [ P times Q]
Probability of a boy and a girl is 2PQ

two girls=[P^2] = 1/4
boy and a girl = 2PQ=1/2
two boys = Q^2= 1/4

Arthur
 
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