Question

The usher at a wedding asked each of the 80 guests whether they were a friend of the bride or of the groom. 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 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, $n(A \cap B)=30$

Therefore:

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

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.

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