Question

Due to a manufacturing​ error, eighteight cans of regular soda were accidentally filled with diet soda and placed into a 2424​-pack. suppose that two cans are randomly selected from the 2424​-pack. complete parts​ (a) through​ (c). ​(a) determine the probability that both contain diet soda. ​p(both ​diet)equals= nothing ​(round to four decimal places as​ needed.) ​(b) determine the probability that both contain regular soda. ​p(both ​regular)equals= nothing ​(round to four decimal places as​ needed.) would this be​ unusual? yes no ​(c) determine the probability that exactly one is diet and exactly one is regular. ​p(one diet and one ​regular)equals= nothing ​(round to four decimal places as​ needed.)

Answer 1

a) the probability would be 0.1014
b) the probability would be 0.4348; no, this would not be unusual
c) the probability would be 0.2319

Explanation
There are 16/24 cans that are regular soda and 8/24 cans that are diet.
a) The probability that the first can is diet would be 8/24.  The probability that the second one is diet after the first one was diet would be 7/23.  The combined probability would be
8/24(7/23) = 56/552 = 0.1014.

b) The probability that the first can is regular would be 16/24.  The probability that the second one is regular would be 15/23.  The combined probability would be
16/24(15/23) = 240/552 = 0.4348.  Since the probability is nearly half, this would not be considered unusual.

c) The probability that the first can is diet would be 8/24.  The probability that the second one is regular after the first can was diet would be 16/23.  This probability would be 
8/24(16/23) = 128/552 = 0.2319.

If we reversed these, and considered getting a regular can first:
The probability of the first can being regular is 16/24.  The probability that the second can is diet after the first one was regular would be 8/23.  The probability would be
16/24(8/23) = 128/552 = 0.2319. The probability for c is the same either way.

Answer 2

Answer:

Part C. you do 1- ((8/24)(7/23)+(16/24)(15/23)=.4638

Step-by-step explanation: