probability and statistics

Question

Find the probability of at least 6 failures in 7 trials of a binomial experiment in which the probability of success in any one trial is 9%. Round to the nearest tenth of a percent

Answer 1

If probability of success is 0.09, then the probability of failure is 0.91. We're wanting at least 6 failures. This means 6 failures or 7 failures. So we would need to use the binomial probability density function for both 6 and 7, and add the results.bility

The general binomial probability density function is

P(X = x) = _nC_x · p^x (1 - p)^{n - x}

So, P(X = 6) = ₇C₆ · 0.91⁶ (0.07)¹ ≈ 0.27826

And P(X = 7) = ₇C₇ · 0.91⁷ (0.07)⁰ ≈ 0.51676

I rounded to 5 decimal places so I was sure my rounding would be ok if I need 3 decimal place. So if we add these, we get 0.27826 + 0.51676 = 0.79502, which rounds to 0.795, or 79.5%.