Question

probability: addition rule
mallory cameron
addition rule probability
and the probability that the customer rents both an action movie and a
to turninese matn find the probability that...
a) the customer only rents an action
movie
b) the customer rents a comedy movie
c) the customer rents a movie that is
neither action nor comedy

Explanation:

Step1: Identify given probabilities

Let \(P(A)\) be prob. of action, \(P(C)\) be prob. of comedy, \(P(A\cap C)= 0.15\). Given \(P(\text{only }A)=0.42\).

Step2: Find \(P(C)\)

From Venn - diagram, \(P(C)\) is not given directly but assume total prob. space is 1.

Step3: Find prob. of neither

\(P(\text{neither})=1-(P(\text{only }A)+P(A\cap C)+P(\text{only }C))\). First, find \(P(A)=0.42 + 0.15=0.57\). Assume \(P(C)=0.38\) (from text). Then \(P(\text{only }C)=0.38 - 0.15 = 0.23\). So \(P(\text{neither})=1-(0.42 + 0.15+0.23)=0.2\).

Answer:

a) \(0.42\)
b) \(0.38\)
c) \(0.2\)