Question

A health spa offers holiday promotional treatment packages at a discount. Its recent tally for 4th of July holiday showed that 18% of the customers received seaweed wraps, 25% received shiatsu massages and 10% received both. What is the probability that a customer selected at random has received either seaweed wrap or shiatsu massage

Answer 1

Answer:

Probability that a customer selected at random has received either seaweed wrap or shiatsu massage is 0.33.

Step-by-step explanation:

We are given that a health spa offers holiday promotional treatment packages at a discount. Its recent tally for 4th of July holiday showed that 18% of the customers received seaweed wraps, 25% received shiatsu massages and 10% received both.

Let Probability that customers received seaweed wraps = P(SW) = 0.18

Probability that customers received shiatsu massages = P(SA) = 0.25

Probability that customers received both seaweed wraps and shiatsu massages = $P(SW \bigcap SM)$ = 0.10

Now, we have to find the probability that a customer selected at random has received either seaweed wrap or shiatsu massage.

So, probability that a customer selected at random has received either seaweed wrap or shiatsu massage is given by = $P(SW \bigcup SM)$

As we know that;

               $P(A \bigcup B) = P(A) + P(B) - P(A \bigcap B)$

So, according to our question;

               $P(SW \bigcup SM) = P(SW) + P(SM) - P(SW \bigcap SM)$

                                       = 0.18 + 0.25 - 0.10

                                       = 0.43 - 0.10 = 0.33

Hence, probability that a customer selected at random has received either seaweed wrap or shiatsu massage is 0.33.