Answer to Question #185730 in Statistics and Probability for Franco

Question

Data shows that 25% of treadmills at a gym have errors in their electronics. A technician randomly selects six treadmills.

10.

The probability that four of these treadmills have errors in their electronics is:

Answer 1

p = 25 % = 0.25

q = 0.75

n = 6

$P(X=4) = C^6_4(0.25)^4(0.75)^{6-4} \\ = \frac{6!}{4!(6-4)!} \times 0.25^4 \times 0.75^2 \\ = 15 \times 0.00390625 \times 0.5625 \\ = 0.0329$