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, n(S)=80
Let the Event (a friend of the bride) =B
Let the Event (a friend of the groom) =G
n(B) =59
n(G)=50
[tex]n(B \cap G)=30[/tex]
Therefore:
[tex]n(B \cup G)=n(B)+n(G)-n(B \cap G)\\n(B \cup G)=59+50-30\\n(B \cup G)=79[/tex]
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(B \cup G) =\dfrac{n(B \cup G) }{n(S)} \\\\=\dfrac{79 }{80}\\\\=0.9875[/tex]
