Question

: A consumer electronics company has observed that 36 percent of their customers purchased a plasma screen television, that 26 percent of their customers purchases a DVR, and 12 percent of their customers purchased both a plasma screen TV and a DVR. Find the probability that a randomly chosen customer either purchases a plasma screen TV or a DVR.

Answer 1

Answer:

The probability that a randomly chosen customer either purchases a plasma screen TV or a DVR is 0.50 or as a percentage 50%.

Step-by-step explanation:

A consumer electronics company has observed that 36 percent of their customers purchased a plasma screen television, that 26 percent of their customers purchases a DVR, and 12 percent of their customers purchased both a plasma screen TV and a DVR. Find the probability that a randomly chosen customer either purchases a plasma screen TV or a DVR.

We have two elements in this set

Customers that purchase a plasma Screen ( S)

Customers that purchase a DVR (D)

From the question:

Customers that purchased a plasma screen television (P) = 36% = 0.36

Customers that purchased a DVR (D)= 26% = 0.26

Customers that purchased a plasma screen television and a DVR = ( S ∩ D) 12% = 0.12

Customers that purchased a plasma screen television = ( S ∪ D)

P ( S ∪ D) = P(S ) + P( D) - P ( S ∩ D)

P ( S ∪ D) = 0.36 +0.26 - 0.12

= 0.62 - 0.12

= 0.50

Converting to percentage = 0.50 × 100 = 50%

Therefore, the probability that a randomly chosen customer either purchases a plasma screen TV or a DVR is 0.50 or as a percentage 50%