Probability homework question help??

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Can someone help me figure this out???

16. A couple plans to have 4 children. If having a boy or girl is equally likely at each birth then:
a. What is the probability of having all girls?

b. What is the probability of having at least 1 child of each gender?

c. What is the probability of getting exactly 2 children of each gender?

d. What is the probability of the first 2 children being the same gender?

e. What is the probability of having at least one child that is gay?

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@mihanni21 ,

There are two equally likely outcomes for each child (boy or girl). Therefore, there are 2*2*2*2=16 possible outcomes:
bbbb
bbbg
bbgb
etc.

Using the table of 16 possible outcomes, determine how many satisfy each question, then divide by the total number of possible outcomes to get the probability. Hint: One of the questions can't be answered with the data that is given.

1 Reply

@markr,

Ok so for a) it would be 4/16
b)2/16
c)2/4
d)2/4
e) can't be answered with the data given

Are those correct?

1 Reply

@mihanni21 ,

Did you write out the full chart?

for a), count the number of times gggg appears, and then divide by the total number of items on the chart.

1 Reply

@DrewDad,

here is the chart I came up with
1) bbbb
2)bbbg
3)bbgb
4)bgbb
5)gbbb
6)gggg
7)gggb
8)ggbg
9)gbgg
10)bggg
11)bbgg
12)ggbb
13)bgbg
14)gbgb
15)gbbg
16)bggb

gggg only appears once??? each combination only appears once??

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@mihanni21 ,

Correct.

(Strictly speaking, this is a list of permutations. In the list, the order of the children matters. If the Position matters, it's a Permutation.)

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@DrewDad,

So, what is the chance of getting all girls?

1 Reply

@DrewDad,

Ok...soo....are the following answers correct??
a) 1/16
b)14/16
c)6/16
d)8/16=1/2
e) cannot be determined with the data given.

1 Reply

@mihanni21 ,

Yes!

The only other suggestion I have is that you reduce your fractions.

1 Reply

That was good mental exercise for a senior like me! LOL

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@DrewDad,

Ok so .....are the following answers all correct??
a)1/16
b)14/16=7/8
c)6/16=3/8
d)8/16=1/2
e) cant be answered with the data given

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@mihanni21 ,

Yes.

1 Reply

@DrewDad,

Great! Thank you so much for walking me through this !!!

1 Reply

@mihanni21 ,

Happy to help.

It's nice to have someone who's willing to put in the effort, instead of just asking for the answer.

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Probability homework question help??

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