The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transporta

Question

The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 10 Southwest flights and observing whether they arrive on time.
Find the probability that exactly 8 flights arrive late.

Answer 1

If you required a particular pattern for the 2 on-time and 8 late flights (such as 2 on time, followed by 8 late), then the probability would be:
(.8^2) (.2^8)

But the on-time and late flights can occur in ANY order, so you need to figure out how many ways that 2 on-time and 8 late flights can be sequenced. This is equal to 45 = (10)(9)/2.

So the answer you want is:
45 (.8^2)(.2^8) = 45 x .64 x .00000256 = .000073728

Answer 2

p = .8, x = # of successes (plane arrives on time)

P(x=2) = 10!/(2!*8!) * .8^2 * .2 ^ 8 = .00007373

Answer 3

You mean The United States Air Force,don't you! ,we even track YOU!

Answer 4

(10c8)*(.2)^8*(.8)^2