LESSON 6 - MUTUALLY EXCLUSIVE EVENTS
EXAMPLE ① The cookie monster’s cookie jar contains 5 chocolate chip, 4 Oreo, and 7 Fudgeo cookies. If he
takes one cookie as a snack, determine the probability that it is:
a) a Fudgeo;
b) an Oreo;
c) a Fudgeo OR an Oreo.
The cookie sets are DISJOINT (ie) there is NO intersection. Therefore the events of choosing the cookies are
MUTUALLY EXCLUSIVE.
ADDITION RULE for MUTUALLY EXCLUSIVE EVENTS
𝑃 𝐴 𝑜𝑟 𝐵 = 𝑃 𝐴 + 𝑃 𝐵
𝑃 𝐴∪𝐵 =𝑃 𝐴 +𝑃 𝐵
Example ② In the toss of two dice, determine the probability of rolling:
a) doubles;
b) a sum of 6;
c) doubles OR a sum of 6.
The events “rolling doubles” or “a sum of 6” are NON-MUTUALLY EXCLUSIVE events.
ADDITION RULE for NON-MUTUALLY EXCLUSIVE EVENTS
𝑃 𝐴 𝑜𝑟 𝐵 = 𝑃 𝐴 + 𝑃 𝐵 − 𝑃 𝐴 𝑎𝑛𝑑 𝐵
𝑃 𝐴∪𝐵 =𝑃 𝐴 +𝑃 𝐵 −𝑃 𝐴∩𝐵
Example ③ One thousand OLMC students were polled as to their TV preferences with the following results:
350 students watched “Big Bang Theory (BBT)”, 650 watched “Modern Family (MF)”, and 230
watched both.
a) Draw a Venn diagram illustrating the
above events.
b) Determine the following probabilities:
i) a student watched BBT;
ii) a student did NOT watch BBT;
iii) a student watched BBT and MF;
iv) a student watched BBT or MF.