Complete Question
The usher at a wedding asked each of the 80 guests whether they were a friend of the bride or of the groom. The results are: 59 for Bride, 50 for Groom, 30 for both. Find the probability that a randomly selected person from this sample was a friend of the bride OR of the groom.
Answer:
0.9875
Step-by-step explanation:
Total Number of Guests which forms the Sample Space, n(S)=80
Let the Event (a friend of the bride) =A
Let the Event (a friend of the groom) =B
n(A) =59
n(B)=50
Friends of both bride and groom, [tex]n(A \cap B)=30[/tex]
Therefore:
[tex]n(A \cup B)=n(A)+n(B)-n(A \cap B)\\n(A \cup B)=59+50-30\\n(A \cup B)=79[/tex]
The number of Guests who was a friend of the bride OR of the groom = 79
Therefore:
The probability that a randomly selected person from this sample was a friend of the bride OR of the groom.
[tex]P(A \cup B) =\dfrac{n(A \cup B) }{n(S)} \\\\=\dfrac{79 }{80}\\\\=0.9875[/tex]
