Question

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. Round to 4 decimal places...n=15​, p=0.8​, x=14
P(14)=enter your response here:

Answer 1

Answer:  0.1319

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Work Shown:

$P(x) = (_n C_x)*(p)^x*(1-p)^{n-x}\\\\P(14) = (_{15} C_{14})*(0.8)^{14}*(1-0.8)^{15-14}\\\\P(14) = 15*(0.8)^{14}*(0.2)^{1}\\\\P(14) \approx 0.13194139533312 \\\\P(14) \approx \boldsymbol{0.1319}$

Side note: you can use the nCr formula to compute $_{15} C_{14}$; however, it's much quicker to use the shortcut formula $_{n} C_{n-1} = n$. You can also use Pascal's Triangle to find the value of $_{15} C_{14}$