I am not getting the above.
Let me calculate the probability of getting 2 successes from 5 Bernoulli trials.
There are total 10 possible outcomes as each trial has two possible outcomes.
The probability of getting one success is P(S1) = No. of successes / no. of total possible outcomes
= 5/10 = 1/2
The probability of getting another success = No. of successes / no. of total possible outcomes
So, the probability of getting two successes = 1/2(4/9)= 2/9
This doesn't match the answer given by the binomial distribution formula.
So, what is wrong here?
I couldn't understand how is binomial distribution sum of n independent Bernoulli trials?
If I denote ith trial by ##X_i ##, then how can k i.e. no. of successes be sum of the trials i.e.∑##_i X_i##?
The Attempt at a Solution