Chapter 6.3 A
1. Zack has applied to both Princeton and Stanford. He thinks that the probability that Princeton
will admit him is 0.4, the probability that Stanford will admit him is 0.5, and the probability that
both will admit him is 0.2.
a) Make a Ven diagram marked with the given probabilities.
b) What is the probability that neither university admits Zack? 𝑃(𝑁𝑒𝑖𝑡ℎ𝑒𝑟 𝑆𝑐ℎ𝑜𝑜𝑙) = 0.3
c) What is the probability that he gets into Stanford but not Princeton?𝑃(𝑂𝑛𝑙𝑦 𝑆𝑡𝑎𝑛𝑓𝑜𝑟𝑑) = 0.3
2. Stephanie is graduating from college. She has studied Biology, Chemistry, and Computing and
hopes to work as a forensic scientist and apply her science background to crime investigation.
Late one night she thinks about some jobs she has applied for. Let A, B, and C be the events that
Stephanie is offered a job by
A = the Connecticut Office of the Chief Medical Examiner
B = the New Jersey Division of Criminal Justice
C = the federal Disaster Mortuary Operations Response Team
Stephanie writes down her personal probabilities for being offered these jobs:
P(A) = 0.6
P(B) = 0.4
P(C) = 0.2
P(A ∩ B) = 0.1
P(A ∩ C) = 0.05
P(B ∩ C) = 0.05
P(A ∩ B ∩ C) = 0
a) Make a venn diagram of the events A, B,
and C. (Look at page 439) Mark the
probabilities of every intersection
involving these events and their
complements.
b) What is the probability that Stephanie is offered at least one of the three jobs?
This is easier if you look at the complement. The complement of being offered at least 1 job
is being offered not job at all. 𝑃(𝑛𝑜 𝑜𝑓𝑓𝑒𝑟) = 0, 𝑠𝑜 1 − 0 =
1. 𝑆ℎ𝑒 𝑖𝑠 𝑔𝑢𝑎𝑟𝑎𝑛𝑡𝑒𝑒𝑑 𝑡𝑜 𝑔𝑒𝑡 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑗𝑜𝑏𝑠.
c) What is the probability that Stephanie is offered both the Connecticut and New Jersey jobs
but no the federal job? 0.1