Question

I'm working on probability HW and working on word problems. Do you have any tips as to how to differentiate between Binomials, Geometric and Negative Binomials when doing word problems .

Answer 1

Binomial is simplest one in this we have number of trials given 'n' and probability of success 'p' and they ask for probability of getting success 'r' times.

For example: When we toss a coin 3 times what's probability of getting 2 heads. Here n = 3, p = 0.5 (because success is getting head, and that is 0.5)

Geometric: Geometric is extended form of Binomial distribution almost same just in this it ask for probability of first success in 'r' th trial.

For example: When we toss a coin 3 times what's the probability of getting 1st head on 2nd toss.

Negative binomial: This is one more step ahead it's same as Geometric it ask for 'k' th success in 'r' th trial.

For example: When we toss a coin 3 times what's the probability of getting 2nd head in 3rd toss.

I took same experiment to explain how it change from one distribution to another. I hope this will help.