An Air Force intercept squadron consists of 16 planes that should always be ready for immediate launch. However, there is a probability of 0.25 that the engines of a particular plane will not start at a given attempt. If this happens, the mechanics must wait 5 minutes before trying to start the engine again. What is the expected number of planes to immediately launch?

Answer: Hello!

The expected value is defined as:

s = ∑xₙpₙ where xₙ is the event, and pₙ is the probability of such an event.

here the events are that the plane is immediately ready with a 0.75 (we can define this event as a 1, this plane counts as one more that can go) and that the plane has a problem with a 0.25 (this event is a 0, if the plane has a problem, it cant launch immediately)

and this is for each of the 16 planes

then the expected value is:

s = 16 * (0.25*0 + 0.75*1) = 16*0.75 = 12

Then the expected number of planes to immediately launch is 12.