Answer:
The probability that at least one movie had seen P(S∪(AD)∪H) = 0.75
Step-by-step explanation:
The total number of movie attendance in the last year n =100
Let 'S' be the event had seen science fiction movie
The probability of that the event had seen science fiction movie
P(S) = 40/100 = 0.4
Let 'AD' be the event had seen adventure movie
the probability of that the event had seen adventure movie
P(AD) =55/100 = 0.55
Let 'H' be the event had seen Horror movie
The probability of that the event had seen Horror movie
P(H) =20/100 = 0.2
given data 25 had seen a science fiction movie and an adventure movie
The probability of that the seen a science fiction movie and an adventure movie
that is P(S∩(AD)) = 25/100=0.25
Given 5 had seen an adventure movie and a horror movie
The probability of that the seen adventure movie and a horror movie
That is P((AD)∩ H) = 5/100=0.05
Given 5 had seen an science movie and a horror movie
The probability of that the seen science movie and a horror movie
That is P((S∩ H) = 15/100=0.15
Given only 5 people had seen a movie from all three categories.
The probability of that the seen a movie from all three categories.
That is P(S∩(AD)∩H) =5/100=0.05
The probability that at least one movie had seen P(S∪(AD)∪H) =
= P(S)+P(AD)+P(H) - P(S∩(AD)-P((AD)∩ H)-P((S∩ H) + P(S∩(AD)∩H)
= 0.4+0.55+0.2-0.25-0.05-0.15+0.05
= 0.75
