Simple question

A

AbdelRahmanShady

Junior Member
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I was watching videos about probability and he gave following problem.
two whales one of them is male what is the probability the other is female.
he said the probabilities are (M, F), (F, M), (M,M). so probability other one is Female is 2/3.

But when I used a tree method all things started failing.
There are two cases first one is male said in question or not with probability 0.5 each
IF it is this male then probability the other one is female is also 0.5 so probability of this branch is 0.5 * 0.5 = 0.25

next case if it is not chosen male
then it might be female with 0.5 chance or male with 0.5 chance and other one must be Male in question with p of 1
so probability of female will be 0.5 * 1 = 0.5
so total probability is 0.5 + 0.25 = 0.75 not 2/3

so what is the problem in my method. Did I miss something
 
This sounds like conditional probability. The problem can be restated this way: "given that one male is already present, what is the probability the other will be female?" This reduces the potential number of possibilities to 3 (MM, MF, FM) with 2 of them having a female.
 
next case if it is not chosen male then it might be female with 0.5 chance
Click to expand...
If it is not a male should not it be a female probability 1?

And another problem: if it is given that one of the whales is a male then the probability of picking a male on the first try is not 0.5.
 
i am saying the chosen male the one mentioned in question

so its probability is 0.5 and the other one may be female or male
 
he said the probabilities are (M, F), (F, M), (M,M). A probability of some event is a real number between 0 and 1 inclusive. How can a probability be (M,F)??
 
In order to see where you went wrong in your tree diagram we need to see your tree diagram, so please post it.
 
OP, you gave a description of your tree in words. It was quite hard to follow, but I think this is similar to what you described...
Rich (BB code): 
                Sex of the second
                given that at
                least one
                must be a male
      First      ----------      Outcomes
      -----                      -------
         
                 /   Male        MM  1/4
               1/2
               / 
      Male    @  
   /           \ 
 1/2           1/2
 /               \   Female      MF  1/4
@
 \               /   Male        FM  1/2
 1/2            1
   \           / 
      Female
The above is wrong. You can't include the "given that" conditional as part of a column heading.

--

I think that conditions have to apply to the whole tree...
Code: 
GIVEN THAT THE FIRST OR SECOND MUST BE MALE...

      First          Second    Outcomes
      -----          ------    --------
         
                 /   Male      MM  1/3
               1/2
               / 
      Male    @  
   /           \ 
 2/3           1/2
 /               \   Female    MF  1/3
@
 \               /   Male      FM  1/3
 1/3            1
   \           / 
      Female

OR draw the tree without any conditional at all...
Code: 
      First          Second    Outcomes
      -----          ------    --------
         
                 /   Male      MM  1/4
               1/2
               / 
      Male    @  
   /           \ 
 1/2           1/2
 /               \   Female    MF  1/4
@
 \               /   Male      FM  1/4
 1/2           1/2
   \           / 
      Female  @  
               \ 
               1/2
                 \   Female    FF  1/4
...and then use P(A given B) = P(A and B) / P(B) where A is the event that at least one is female and B is the event that at least one is male. Personally, to avoid confusion, this is the approach that I'd use.
 
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