# Calculating probability of getting at least 3 red ball drawn from a bag having 6 red ball,5 blue,4 green in 5th attempt.

Mathematics Asked by Rajakr on December 30, 2020

There are 6 red balls,5 blue balls,and 4 green balls in a bag. What is the probability of drawing at least 3 red ball in 5th attempt. Assume balls are drawn with replacement

I tried to use binomial concept and conditional probability formula. As probability of drawing red ball is 6/17,then took case for if balls drawn are 3red & 4red & 5red & 6red. & Then summed all probability but it got very lengthy and messed up.

If you try to sum up the probabilities of drawing exactly $$3$$ red balls on the third, fourth or fifth attempt, you will find it a bit tricky because you'll always have to keep in mind that the last trial $$(say, k),$$must be a win, and work out the combinations for $$k-1$$ trials followed by a win on the $$k_{th}$$ trial, which can become messy.

But if you understand that in $$5$$ attempts, you can have at most $$2$$ failures, then it becomes very simple.

$$dbinom50 q^0p^5 + dbinom51 q^1p^4 +dbinom52 q^2p^3$$, and evaluate

Answered by true blue anil on December 30, 2020