Two Conditional Probability Examples (what's the difference???)

We investigate two basic conditional probability examples that are ALMOST identical but slightly different. We look at the probability of two children both being girls given either that we are told one of the two kids is a girl, or that we are told the oldest of the two kids is a girl.

Conditional Probability Formula: P(A|B) = P(A and B)/P(B)

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[gbnas]

I'm a stats tutor, and this is helping me relearn probability and get examples of how to explain it

[badrang]

Beautiful example and distinction, thanks so much for sharing. Conditional and Bayesian probability really messes with my head so it means the world that videos like yours are out there; thank you very much.

[bedrie]

The common sense solution for Ex 1:
1. For 2 children of 2 genders, we have 2^2 = 4 possible outcomes (GG, GB, BG, BB)

2. We know there is at least one girl, so 'All boys (BB)'
outcome becomes invalid
So -> All possible outcomes = 4 - 1 = 3

3. Of these possible outcomes, we are interested in 'All girls (GG)' outcome only
So -> Number of outcomes we are interested in = 1

4. (Number of outcomes we are interested in) / (All possible outcomes) = 1 / 3

[abhi]

You mode complex topic looks so simple with your example. Great video.

[xX_dash_Xx]

Wouldn't the set of all possible offspring be a combination, not a permutation? Instead of GG, GB, BG, BB we would have GG, GB, BB. Then the intuitive answer of 50% for the first example question would make sense:
P(2G | at least 1G) = (1/3)/(2/3) = 0.5

I don't see why it is a permutation, that is what is tripping me up.

[_ngecu]

Example one breakdown:
P(A/B)=P(AnB)/P(B)

NUMERATOR:
The are 2 people(GG, GB, BG, BB) so each probability of 2 girls is GG: 1/4

For at least 1 girl the BB is considered void since it has no girls involved so the probability is out of 3 choices."For at least 1 girl" means 1 girl and above making the probability 3/3 since the rest all have a girl i.e GG, GB and BG
DENOMINATOR:
Probability of at least a girl, we also consider the boys since it is not conditional making it 3/4

[farhatasneem]

But aren't BG and GB the same outcomes? Is the order important?

[cooliojones]

🎯 Key Takeaways for quick navigation:

00:00 📊 Conditional probability involves calculating the likelihood of an event A given that event B has occurred.
01:57 🧮 When at least one girl is known to be in a family with two children, the probability that both children are girls is 1/4.
04:42 🔄 The probability changes when the condition specifies the older child is a girl, resulting in a 1/2 chance of both children being girls, highlighting the importance of clarifying conditions in conditional probability calculations.

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[sherazahmed]

smh makes sense when you do it but im always lost whenever i try doin it myself. Lord have mercy when i start studying bayes theoram

[waknuktwo]

Clear explanations, easy to follow examples and engaging teaching well done and thank you.

[programminglife]

In the first example, aren’t they same things G, B and B, G. Because when it’s told that there must be at least one girl it means we have two possible space. One girl one boy and two girl. And question is what is the probability of two girl. It’s obviously 1/2. There is no permutation

[sudarshan]

Thanks, this helps me a lot.
Love from India 🇮🇳

[rahulsabinkar]

Thanks for these videos! I got this subject called "Computer Oriented Statistical Methods" and these topics are in curriculum. Tomorrow I got the exam for it and your videos helped me revise it for me.

[mrrule]

Very simple and professional !! I watch this to remember what I learnt 3 years ago in faculty.

[chessleochessleo]

nice calculation. I think there was a school math text many years ago where the prof gave a different answer. (something about a girl walking into the room and parent saying she is their eldest child)

[imran_v.]

2:31 having 1 boy and I girl isn't same as 1 girl and 1 boy?

[FarahNazifa]

Wow man! You are just brilliant! I wish you have so many statistical videos describing the chapters and show few examples to the topics. :))

[NikSargent]

It’s amazing how obvious the second example is when drawn out, yet how counterintuitive it seems.
Tying the “given” to one specific child (the older girl) rather than either girl, feels like it should reduce the probabilities and yet it increases them. Hurts the head :)

[Rahulkumar-czjj]

this was the best example of all time
after two days I have my maths exam and this video just saved my 2 +hour
thank you sir

[vspianist]

I am so confused when I try to do these problems. How do I KNOW when BG is the SAME as GB or they count as two different ones