Suppose I have a bag. It contains 2 red balls and 5 blue balls.
If I draw two balls from the bag consecutively, with replacement, the possible outcomes of this experiment can be :- {RR,RB,BR,BB}, where R is the event of getting red ball and B is the event of getting blue ball.
So the probability of both drawn balls being red can be :
P(x)=n(x)/n(S)...where x represents the event, in which both drawn balls are red.
So, P(x)=1/4 ...........(1)
But, I found that, P(X)=P(R intersection B), as R and B event happening simultaneously.
So, P(X) becomes 4/49 .......(2)
In my 1st approach, I am considering the event of both balls being red and it is same in my 2nd approch also
Although, there is a huge discrimancy in the probability, between my two approaches
Why is this happening and which approach should I use??