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## Homework Statement

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

= 4/9

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##?

## Homework Equations

## The Attempt at a Solution

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