Question

Due to a manufacturing error, four cans of regular soda were accidentally filled with diet soda and placed into an 18 pack. Suppose that two cans are randomly selected from the 18 pack.a. Determine the probability that both contain diet soda. (Round to four decimal places as needed.)b. Determine the probability that both contain regular soda. (Round to four decimal places as needed.)Would this be unusual?A. YesB. Noc. Determine the probability that exactly one is diet and exactly one is regular. (Round to four decimal places as needed.)

Answer 1

Answer:

(a)  0.5948

(b ) 0.0392;  A. Yes , because the probability is less than 0.05

(c) 0.3660

Step-by-step explanation:

Probability of regular soda; P (regular soda) = 4/18

Probability of diet soda; P (diet soda) = 14/18

Let R = Outcome of Regular soda

      D = Outcome of Diet soda

P (R) = 4/18

P(D) = 14/18

Note that it is a probability without replacement situation

The total sample space for randomly selecting two cans from the 18 packs is given as :

R     R

R     D

D    R

D    D

(a.) Determine the probability that both contain diet soda.

P(both Diet Soda) = P (DD)

                             =   14/18 x 13/17

                             = 0.59477

                             ≈ 0.5948

(b.) Determine the probability that both contain regular soda.

 P (both regular soda) = P (R R)

                                     =  4/18 x 3/17

                                     = 0.039215

                                     ≈ 0.0392

Would this be unusual?

A. Yes , because the probability is less than 0.05

(c.)  Determine the probability that exactly one is diet and exactly one is regular

P(exactly one regular) = P(RD) + P(DR)

                                    =   (4/18 x 14/17) + (14/18 x4/17)

                                    = 0.36601

                                    ≈ 0.3660