Question

Due to a manufacturing error, eight cans of regular soda were accidentally filled with diet soda and placed into a 24-pack. Suppose that two cans are randomly selected from the 24-pack. Complete parts (a) through (C). (a) Determine the probability that both contain diet soda. P(both diet) = 0.1014 (Round to four decimal places as needed.) (b) Determine the probability that both contain regular soda. P(both regular) = 0.4348 (Round to four decimal places as needed.) Would this be unusual? No Yes O (c) Determine the probability that exactly one is diet and exactly one is regular Plone diet and one regular) = 0.4638 (Round to four decimal places as needed.)

Answer 1

The probability that both contain regular soda is not unusual as it is greater than 0.05. So, no this would be unusual.

Given:

Total cans = 24

Number of diet sodas = 8

Number of regular soda = 24 - 8 = 16

x = Number of cans selected from 24 cans = 2

(a)

P( both diet) = .........?

P( both diet) = P(First Diet) * P(Second Diet | First Diet)

P( both diet) = 8/24 * 7/23

P( both diet) = 0.1014

(b)

P( Both regular) = ........?

P( Both regular) = P( First regular ) * P(Second Regular| First regular)

P( Both regular) = 16/24 * 15/23

P( Both regular) = 0.4348

Since the probability is > 0.05, it is not unusual.

(c)

P( One Diet and One Regular) = ............?

P( One Diet and One Regular) = P( First Diet and Second Regular or First Regular and Second Diet)

P( One Diet and One Regular) = P( First Diet and Second Regular) + P(First Regular and Second Diet)

P( One Diet and One Regular) = [ 8/24  * 16/23 ] + [ 16/24 * 8/23 ]

P( One Diet and One Regular) = [ 0.2319 ] + [ 0.2319 ]

P( One Diet and One Regular) = 0.4638

To learn more about the probability visit: https://brainly.com/question/11234923

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