If A and B are two events, the probability that exactly one of them occurs is given by

• A

  $\mathrm{P}\left(\mathrm{A}\right)+\mathrm{P}\left(\mathrm{B}\right)-2\mathrm{P}(\mathrm{A}\cap \mathrm{B})$

• B

  $\mathrm{P}(\mathrm{A}\cap \overline{\mathrm{B}})+\mathrm{P}(\overline{\mathrm{A}}\cap \mathrm{B})$

• C

  $\mathrm{P}(\mathrm{A}\cup \mathrm{B})-\mathrm{P}(\mathrm{A}\cap \mathrm{B})$

• D

  $\mathrm{P}\left(\overline{\mathrm{A}}\right)+\mathrm{P}\left(\overline{\mathrm{B}}\right)-2\mathrm{P}(\overline{\mathrm{A}}\cap \overline{\mathrm{B}})$