Question

what is the probability that in a family of three children that the third child is a girl

Answer 1

This tree diagram may help.

Answer 2

If there are 8 outcomes and 4 of them have a girl as the third child, then would the probability be 4/8 = 1/2?

Answer 3

Chance of a boy or girl is roughly 50%, and is independent of whether the other two children are boys, girls, or whatever.

Directrix's tree diagram can confirm that, but since they're independent events, it isn't necessary.

Answer 4

I don't see any restrictions on the gender of the first two kids.

Answer 5

@Directrix they're independent events. The first 1000 children could be girl, and the third child is still 50-50 on being a girl.

Answer 6

I see this as a classic coin-toss problem:
Regardless of how many times a fair coin is tossed, what are the odds that the next toss will be a head?

Answer 7

Right. I just like to look at diagrams to clarify my thinking.

Answer 8

This is the same as saying "you flip a coin 1000 times, and the first 999 are heads-what is the chance the 1000th is a head? The 1500th?"

Answer 9

Speaking of coin toss problems, we should help out the person who posted this:

http://openstudy.com/study#/updates/516d10fee4b063fcbbbcc67e

I could probably draw a tree diagram, if needed. :)

Answer 10

A tree diagram would be handy in that question :)

Answer 11

What does "sample space" mean in that question?

I get 50% for B, and 25% for C

Answer 12

Sample Spaces
the set of all possible outcomes of an experiment or series of trials. For example, coin toss:{h, t} ; roll of a single die:{1, 2, 3, 4, 5, 6}

http://ededu.net/Main/Math/151stat/sampleSpaces.html

Answer 13

Oh, okay! :-)

So we can use your example for A:
coin toss:{h, t} ; roll of a single die:{1, 2, 3, 4, 5, 6}

Which still gives me 50% for B, and 25% for C :-)

Answer 14

And thank you for explaining that, BTW! :-)

Answer 15

@qweqwe123123123123111 I don't see how you got 50% and 25%.

Answer 16

Re question B:
He only specified whether an odd number was rolled. This makes the values of the coin toss irrelevant.
The coin toss has 100% probability of being a head or tail.
The die roll has a 50% probability of coming up odd.
The next coin toss has 100% probability that it will be a head or tail.

That's 100% * 50% * 100% = 50%

Answer 17

I was too lazy to read all the responses, so this might have been already said, but I'll say it anyways.
Looking at a single case, we have to ignore the others. It doesnt matter if the last 10 coin flips have been heads, the next one is still 50/50 of being heads or tails. So the dance of the third child being a girl would be %50 because you could either have a boy, or a girl (and genetically speaking, each is equally likely).

Answer 18

Re question C:
Here he specified a T was tossed, followed by an even roll, and no definition of the 2nd toss.
The probability of flipping a T is 50%
The probability of rolling an even number is also 50%
The 2nd toss has a 100% probability of being H or T

This makes 50% * 50% * 100% = 25%

Answer 19

^ @qweqwe123123123123111 that's actually not what c asks for (your answer is correct, method is not quite)

"let B be the event exactly one T flipped and the number rolled is even. Find prob. event B."

ie the there has to be one T, either on the first or second toss.

Post this in the other question :P

Answer 20

There's an odd reason I'm posting it here. Directrix referenced the other problem from here, and posting my comments on that post would constitute "just giving the answer".
So I've been posting my comments here where Directrix first addressed the issue.

Answer 21

Fair enough. Your answer for c was still correct, because the chance of getting exactly one T is 50%. Since you can get either TH or HT, out of the possible HH, TT, TH, HT.