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

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.

Mathematics Asked by Rajakr on December 30, 2020

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

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