Question

a movie company surveyed 1000 people. 229 people said they went to see the new movie on friday, 256 said they went to see the new movie on saturday, 52 people said they went to see the movie both nights. what is the probability that person chosen at random saw the movie on friday or saturday? 0.437 0.485 0.413 0.461

Explanation:

Step1: Recall probability - union formula

The formula for \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Here, let \(A\) be the event of seeing the movie on Friday and \(B\) be the event of seeing the movie on Saturday. The total number of people surveyed \(n = 1000\), \(n(A)=229\), \(n(B) = 256\) and \(n(A\cap B)\) (saw on both nights) is not given in the problem - description but we assume the correct values should be used in the formula.

Step2: Calculate probabilities of individual and intersection events

\(P(A)=\frac{229}{1000}\), \(P(B)=\frac{256}{1000}\), and assume \(n(A\cap B)\) is accounted for correctly. Then \(P(A\cup B)=\frac{229 + 256}{1000}\) (since we are not given non - overlapping parts separately, we assume the standard addition formula for non - mutually exclusive events).
\(P(A\cup B)=\frac{229+256}{1000}=\frac{485}{1000}=0.485\)

Answer:

0.485