Question

I like to compete in apple bobbing competititons. Everytime I dunk my head underwater to get an apple, I have a probability of 1/5 of successfully retrieving the apple with my teeth. I win the competition after successfully retrieving 3 apples.

(a) Name the probability distribution that governs the number of times I need to dunk my head to get 3 apples.

(b) Compute the probability that I retrieve my third apple on the 6th attempt.

Please write neatly as I have difficulty reading sloppy handwriting. The more detail the better :) Thanks xx

Answer 1

a)

here this is negative binomial with parameter r=3 and p=1/5

b)

P( I retrieve my third apple on the 6th attempt ) =P(2 apples in first 5 attempts and 3rd apple on 6th attempt) =((5C2)*(1/5)²*(4/5)³)*(1/5)=0.0989