Question

According to a recent report, Pandora and Spotify are the most used music-streaming apps. A group of Statistics students surveyed all the seniors in their school and found that 68% use Pandora, 38% use Spotify, and 24% use both. Suppose we select a senior at random. a) Make a Venn diagram to display the sample space of this chance process using the events P: uses Pandora and S: uses Spotify. b) Find the probability that the person uses neither Pandora nor Spotify.

Answer 1

a) The Venn diagram for this scenario can be drawn with two circles, one for Pandora (P) and one for Spotify (S), and their intersection indicating those who use both.

b) The probability that the person uses neither Pandora nor Spotify is 0.18 or 18%.

a) Venn Diagram:

Let's use P to represent the event that a senior uses Pandora, and S to represent the event that a senior uses Spotify. The intersection of P and S, denoted by P∩S, represents seniors who use both Pandora and Spotify.

The Venn diagram for this scenario can be drawn with two circles, one for Pandora (P) and one for Spotify (S), and their intersection indicating those who use both.

b) Probability of using neither Pandora nor Spotify:

To find the probability that a randomly selected senior uses neither Pandora nor Spotify, we need to consider the complement of the event "uses either Pandora or Spotify."

Let A be the event that a senior uses either Pandora or Spotify. The probability of A is the sum of the probabilities of using Pandora and using Spotify minus the probability of using both:

P(A)=P(P)+P(S)−P(P∩S)

P(A)=0.68+0.38−0.24

P(A)=0.82

Now, the probability of the complement event (not using either) is given by:

P(not A)=1−P(A)

P(not A)=1−0.82

P(not A)=0.18

Therefore, the probability that the person uses neither Pandora nor Spotify is 0.18 or 18%.