let’s say that you have ingested a poisonous plant and the only way to save your self is to ingest some element that is found in a female frog. Now the female and male frog look exactly alike and the only difference is that the male frog croaks little differently. Now that you are running out of time you spot a frog to your right and you have been slightly relieved and start running towards that frog on the right. Just while you start running, you hear a croak from your left and you spot two frogs there. Now in this situation you have two options: CASE A – go to right where there is one frog, or CASE B – go to left, where there are two frogs. If your answer is B, then you are right. It comes down to correctly calculating the odds one has.
But hoe does one reach this conclusion and what is it that makes for a wrong decision?
Common Ways Of Wrongly Solving The Problem
Wrong Answer One
assuming that there are same number of male and females frogs present, the probability that you pick a frog and It turns out to be of either sex is one in two. Which makes it a 0.5% chance and which means that it is 50-50. This would work in Case A (one frog, right side), but not in Case B (two frogs to your left).
Wrong Answer Two
In Case B, you figured that one of the frogs is male through its croak. But what is the probability that both of them are male? We established that the probability of the frogs from either of the genders is 0.5%, then the two together would be 0.25% (one in four or 25%), which leaves a 75% chance of getting a female frog.
Right Answer Conditional Probality
If one goes ahead with CASE B, they have a two in three chance of surviving which constitutes to 67%. In Case B, there could be many a combination in terms of male and female in which the frogs could be present in a pair. This set of combination make for a – Sample Space. These combinations of the Sample Space are as follows: 1. Male, Female. 2. Male, Male. 3. Female, Female. 4. Female, Male. Out of these stated combinations, we can see that only one of them gives us two males. Which makes us question that why was the – Wrong Answer Two Assumption wrong about 75% chance? Here we have forgotten about the croak that is made by one of the frogs.
This is give away that one the frogs on our left is a male, which means that it cannot a pair of female frogs, hence eliminating that probability. This ultimately leave us with three combinations in the sample space. Now, even out of the three left, we have one combination that has a chance of getting two males, which constitutes to 67% of the chance of getting a female.
Therefore, conditional probability takes in note a large sample space which looks at every possibility, in that sample. And with the information that is additional to the sample, helps eliminate the possibilities. In return increasing the chance of getting the right answer and eliminating errors