Binomial Probability help please. (1 Viewer)

[Aysce]

Assume that the probability that a child is female is 1/2, and that sex is independent from child to child. Giving your answers are fractions in simplest form, find the probability that in a family of five children:

b. There are two girls and three boys

Well I'm going to show my working just so you guys can know how I am doing it.

(5C2 * (1/2)^2 * (1/2)^3) + (3C3 * (1/2)^3 *1) = 7/16

Answer = 5/16.

Kinda confuzzled so I just thought that you first find the chance of two girls and then you find the chance of getting 3 boys but obviously that's wrong..

 

[Carrotsticks]

You should not have added the (3C3 * (1/2)^3 *1).

Reason is because in your expression (note the part I bolded):

(5C2 * (1/2)^2 * (1/2)^3)

Since you have chosen two of the kids to be girls (from your choice 5C2), this FORCES the other 3 children to be boys (unless there is another gender).

So you essentially double counted the probability of the boys. The second expression you added was redundant.

 

[darkphoenix]

Its 5C2(0.5)^2(0.5)^３＝　５／１６

If p is the probability of success and q is the probability of failure for an
event, then the probability of r successes in n independent events is given by
P r successes ｎＣｒ　Ｐ＾ｒ　ｑ＾（ｎ－ｒ）

 

[Aysce]

You should not have added the (3C3 * (1/2)^3 *1).

Reason is because in your expression (note the part I bolded):

(5C2 * (1/2)^2 * (1/2)^3)

Since you have chosen two of the kids to be girls (from your choice 5C2), this FORCES the other 3 children to be boys (unless there is another gender).

So you essentially double counted the probability of the boys. The second expression you added was redundant.

Hey Carrot, thanks for helping! Although the main problem with what I have in general is the language and when to use certain things. So what I just realised was that the question says AND so wouldn't it be multiplying?

 

[Carrotsticks]

Hey Carrot, thanks for helping! Although the main problem with what I have in general is the language and when to use certain things. So what I just realised was that the question says AND so wouldn't it be multiplying?

I understand where the confusion occurred.

You multiply the probabilities when you have several things happening in ONE event.

Don't think about it as "Okay it has X word, I therefore must add/multiply the probabilities". Think about it logically.

In this case, we take the ONE event to be the moment the mother finishes popping out all 5 children.

You asked "wouldn't it be multiplying?".

The answer is yes, and you did in fact do it already!

When you said (5C2 * (1/2)^2 * (1/2)^3), you multiplied the probabilities!

This is because like I said, we take ONE event to be when all 5 kids are done.

Suppose the question was "What is the probability of the mother either having 2 girls 3 boys, OR 2 boys 3 girls"

We take 1 event to be the 2 girls 3 boys, then the other to be 2 boys 3 girls.

Then you find the probability of each, then you add it up because they are SEPARATE events.

Sorry in advance if I am ambiguous with my explanation, I just woke up from a 2 hr nap and I feel absolutely terrible.

 

[Aysce]

I understand where the confusion occurred.

You multiply the probabilities when you have several things happening in ONE event.

Don't think about it as "Okay it has X word, I therefore must add/multiply the probabilities". Think about it logically.

In this case, we take the ONE event to be the moment the mother finishes popping out all 5 children.

You asked "wouldn't it be multiplying?".

The answer is yes, and you did in fact do it already!

When you said (5C2 * (1/2)^2 * (1/2)^3), you multiplied the probabilities!

This is because like I said, we take ONE event to be when all 5 kids are done.

Suppose the question was "What is the probability of the mother either having 2 girls 3 boys, OR 2 boys 3 girls"

We take 1 event to be the 2 girls 3 boys, then the other to be 2 boys 3 girls.

Then you find the probability of each, then you add it up because they are SEPARATE events.

Sorry in advance if I am ambiguous with my explanation, I just woke up from a 2 hr nap and I feel absolutely terrible.

Oooh okay, I get it. When you're referring to those separate events, you also mean those that are mutually exclusive?

 

[Carrotsticks]

Oooh okay, I get it. When you're referring to those separate events, you also mean those that are mutually exclusive?

Yep =)

Imagine picking coloured marbles from 2 separate jars.

How could me getting X red marbles possible affect me getting Y blue marbles unless the process of getting X red marbles is unusually tiring, thus affecting chances of acquiring Y marbles etc.