Let E be the event that a corn crop has an infestation of ear worms, and let B be the event that a corn crop has an infestation of corn borers. Suppose that P (E) = 0.24, P (B) = 0.16, and P (E and B) = 0.13. Find the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both.

The probability that a corn crop has either an ear worm infestation, a corn borer infestation

P (EUB) = 0.27

Step-by-step explanation:

Explanation:-

Addition theorem on probability:-

If S is a sample space, and E, F are any events in S then

P (EUF) = P (E) + P (F) - P (E n F)

Let 'E' be the event that a corn crop has an infestation of ear worms

let 'B' be the event that a corn crop has an infestation of corn bores

P (EUB) = P (E) + P (B) - P (E n B)

given P (E) = 0.24 and P (B) = 0.16 and P (E n B) = 0.13

P (EUB) = P (E) + P (B) - P (E n B)

P (EUB) = 0.24 + 0.16 - 0.13

= 0.27

The probability that a corn crop has either an ear worm infestation, a corn borer infestation

P (EUB) = 0.27