1. ## Binomial probability problem

A pioneer was panning gold in Qinhai and only 2% chance on the average that he found gold in the past many years. What is the chance for him to find gold in 28 pans or more out of the next 1000 trials?

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I wonder if I should use the binomial probability to obtain the answer. If so, does it mean that I have to calculate all the 28 probabities to do it?
p = 0.02, q = 0.98
1 - (q^1000 + 1000*q^999*p + 499500*q^998*p^2 + ... )

2. Originally Posted by calculus2008
A pioneer was panning gold in Qinhai and only 2% chance on the average that he found gold in the past many years. What is the chance for him to find gold in 28 pans or more out of the next 1000 trials?

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I wonder if I should use the binomial probability to obtain the answer. If so, does it mean that I have to calculate all the 28 probabities to do it?
p = 0.02, q = 0.98

1 - (q^1000 + 1000*q^999*p + 499500*q^998*p^2 + ... )
You're probably expected to either use technology or to use the normal approximation to the binomial distribution.

Use of the latter is OK since the rule of thumb (that the approximation should only be used when both np > 5 and nq > 5) is satisfied.