Let us take a 100 people who are going to toss a coin randomly twice ,now about 50 people(50% of sample space) get heads on average ,now on second toss 50% of that 50% will get Heads again ,so it makes 50% of 50% of Sample Space the number of people who get heads twice in a row.
Now if I apply the same logic for finding the probability of two men having color Blindness given that there is a probability that a man in random has 8% chance of having Color Blindness,if I take the First person there is 8% chance he is color blind now I multiplying the chances of 2nd man having Color Blindness ,I get the Chance of those two men having Color Blindness ,but it's not transparent how multiplying them gives me probability of two men having Color Blindness ,I can't understand as clearly as the example with coin flip.
Let's take a square .
1)The square as a whole talks about the likelihood of a person being Colorblind or not .
2)According to the question ,there is a 92% chance that this person is not colorblind ,there is an 8% of him being Colorblind.Sonin order to represent this in terms of area of square ,I consider a strip of rectangle to represent the chances of him being Colorblind.I am planning to position this strip in such a way that it is to the left of the square, meaning that it has the same length as the square ,so in order for the area to be 8% ,the breadth must be 8% of the breadth of the square.So this represents a person's chances of being Colorblind.
Now I take another square ,this represents the chances of the other person being Colorblind ,he has the same chances of being Colorblind ,now this time I consider a strip of rectangle at the top ,meaning that it has the same breadth ,so for the area to be 8%,the length must be 8% of original length of the square. So now we have two square (two people and their chances of being Colorblind),each having a strip of rectangles ,each representing the chances of a person being Colorblind ,1st rectangle has its breadth the 8% of original breadth,second rectangle has its length the 8% of original breadth .
If I place one square over the another the common area has an length that is 8% of original length and a breadth that is 8% of original breadth . So the area will be new breadth (8% of original breadth)*new length(8% of original length).Multiplying these values we see that the common area is 6.4% of the original area,this area represents the chances of two person being Colorblind.