Question

You pick 154 balls one by one with replacement from a bag. The bag has 3 yellow, 2 orange and 8 green balls. You count how many orange and how many yellow balls you get. This is a binomial distribution.

TRUE OR FALSE

Answer 1

Yes this is a Binomial Distribution.

154 Balls are drawn from a bag with replacement i.e. their color is noted and again put back in the bag before another draw.

The bag has 3 Yellow balls, 2 orange balls and 8 green balls i.e. there are (3+2+8) =13 balls in total in the bag.

Here we draw 154 balls which can be considered as total no. of samples.

Then we count the no. of orange balls once and then yellow balls.

Let us consider the events of getting a yellow in i^th draw be XI

Then the probability of getting a yellow ball in i^th draw (or any draw) is= 1/3

Let us consider the events of getting an Orange ball in i^th draw is Y_I

Then the probability of getting a orange ball in i^th draw (or any draw) is= ½

Now the random variables X_i and Y_i are Bernoulli Random variables.

We here draw 154 balls. So i= 1(1)154

The total no. of Yellow balls we get after counting is denoted by the random variable,

The total no. of orange balls we get after counting is denoted by the random variable,

We know that the sum of Bernoulli random variables is a Binomial Random variable.

So

And