Question

The usher at a wedding asked each of the 808080 guests whether they were a friend of the bride or of the groom. Here are the results:Find the probability that a randomly selected person from this sample was a friend of the bride OR of the groom.

Answer 1

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

$n(B \cap G)=30$

Therefore:

$n(B \cup G)=n(B)+n(G)-n(B \cap G)\\n(B \cup G)=59+50-30\\n(B \cup G)=79$

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.

$P(B \cup G) =\dfrac{n(B \cup G) }{n(S)} \\\\=\dfrac{79 }{80}\\\\=0.9875$